Geochemistry of Radioactive Isotopes

*Salih Muhammad Awadh*

#### **Abstract**

The chapter targeted the geochemistry of radioactive isotopes dealing with multidisciplinary topics and focusing on geochronology and tracer studies. The most common subjects are presented to include the basic principles of radioactive isotopes. The radioactive decay, the parent nuclide, the SI unit of radioactive decay as well as the historical discovery of radioactivity, the neutrons and protons in atomic nuclei, alpha and beta particles, gamma rays, electromagnetic radiation, decay and mode of decay, chain of decay, decay rates, decay timing, principle of dating, radiometric dating, isotope systems, the Rb/Sr System, the U, Th, Pb System, the age of the earth, Sm-Nd dating, K-Ar dating, 14Carbon dating, the geochron, all those were included overall.

**Keywords:** geochemistry, isotopes, radioactive isotope, parent nuclide, dating

#### **1. Introduction**

The process in which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves known as radioactive decay that causes the energy loss from the parent nuclide converting it to daughter nuclide [1]. This chapter has been authorized based mainly on published reference focusing on some basic properties and principles of radiation and how to use this phenomenon for the estimation the absolute geological age depending on the isotope half-life and provides brief summary of only a very few examples of dating applications. Geochronology and tracer studies are two principle applications of geochemistry of radiogenic isotope. Geochronology goes to estimate the absolute time based on the radioactive rate decay from the beginning of decay to its daughter by knowing how much nuclides have decayed. Tracer application relies on the variation in ratio of the radiogenic daughter isotope to other isotopes of the element. The purpose of authoring this chapter is to help those who are interested in this field and to provide what is useful and brief in a simplified way away from the complexity.

#### **2. Radioactive decay and natural radioactive isotopes**

The radioactive decay (a phenomenon of natural and artificial) means loss of energy that results in an atom named the parent nuclide converting it to an atom of a different type, called the daughter nuclide. The 14C is a parent, emits radiation and transforms to a 14N representing a daughter [2]. Accordingly, it is easy to


**4. Alpha particles**

*Geochemistry of Radioactive Isotopes*

*DOI: http://dx.doi.org/10.5772/intechopen.91616*

nucleus.

(**Figure 3**).

**6. Gamma ray**

**Figure 3.** *Bata radiation.*

**121**

**7. Modes of decay**

**5. Beta particles**

They are particles (α) emitted during the radioactive decay from the nucleus consisting of two protons and two neutrons tightly bound together (**Figure 2**). Such this decay is known as alpha-decay. All chemical elements above Pb, in the Periodic Table have at least one isotope which decays by emitting alpha particles. This process is relatively rare due it requires high energy to release two neutrons and two protons out of a nucleus. The alpha particle is expressed as an identical to a helium

They are also known as beta ray or beta radiation, symbolized by β. Beta has high-energy, high-speed electron or positron emitted during decay process of a nuclei and give β and β+, which yield electrons and positrons respectively

Gamma ray is also named gamma radiation symbolized with γ which is an electromagnetic radiation (**Figure 4**) emitting from the radioactive decay of atomic

Different decay reactions of the radionuclides, the mass number A and atomic

number Z of nucleus defined as A, Z are presented in **Table 1**. The column

nuclei [3]. This type of radiation is very common.

understand that the radioactivity decay is that process by which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. Radioactive elements and their radiogenic daughters as well as the radiogenic and radioactive are illustrated in **Figure 1**.

#### **3. Unit of radioactive decay and activity measurements**

The becquerel (symbol Bq) is typically used as a SI unit of radioactive decay and it is defined as one decay/second. The Bq is just a tiny measure of activity; a small part of tera-becquerel (TBq) or giga-becquerel (GBq) that is commonly used. The curie (Ci) is an another unit of radioactivity that was basically defined as the activity of 1 g of pure radium 226Ra. Currently, The Bq is ordinary equal to number of disintegrations per second; where Ci is equal to 3.7 1010 disintegrations per second. Low activities are also measured in disintegrations per minute (dpm) [2]. The name of the unit "becquerel" is originated and belonging to the Henri Becquere l, a French scientist, who discovered radiation while he working on phosphorescent materials in 1896. Later, many contributions by Becquerel, Marie Curie, Pierre Curie, Ernest Rutherford and others discovered that radioactivity was significantly more complicated [2].

**Figure 2.** *Alpha particle represents the helium atom nuclei.*

### **4. Alpha particles**

They are particles (α) emitted during the radioactive decay from the nucleus consisting of two protons and two neutrons tightly bound together (**Figure 2**). Such this decay is known as alpha-decay. All chemical elements above Pb, in the Periodic Table have at least one isotope which decays by emitting alpha particles. This process is relatively rare due it requires high energy to release two neutrons and two protons out of a nucleus. The alpha particle is expressed as an identical to a helium nucleus.

### **5. Beta particles**

understand that the radioactivity decay is that process by which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. Radioactive elements and their radiogenic daughters as well as the

The becquerel (symbol Bq) is typically used as a SI unit of radioactive decay and it is defined as one decay/second. The Bq is just a tiny measure of activity; a small part of tera-becquerel (TBq) or giga-becquerel (GBq) that is commonly used. The curie (Ci) is an another unit of radioactivity that was basically defined as the activity of 1 g of pure radium 226Ra. Currently, The Bq is ordinary equal to number of disintegrations per second; where Ci is equal to 3.7 1010 disintegrations per second. Low activities are also measured in disintegrations per minute (dpm) [2]. The name of the unit "becquerel" is originated and belonging to the Henri Becquere l, a French scientist, who discovered radiation while he working on phosphorescent materials in 1896. Later, many contributions by Becquerel, Marie Curie, Pierre Curie, Ernest Rutherford and others discovered that radioactivity was significantly

radiogenic and radioactive are illustrated in **Figure 1**.

more complicated [2].

**Figure 2.**

**120**

*Alpha particle represents the helium atom nuclei.*

**Figure 1.**

*Geochemistry*

**3. Unit of radioactive decay and activity measurements**

*Periodic table showing the elements of natural radioactive isotopes and their daughters.*

They are also known as beta ray or beta radiation, symbolized by β. Beta has high-energy, high-speed electron or positron emitted during decay process of a nuclei and give β and β+, which yield electrons and positrons respectively (**Figure 3**).

**Figure 3.** *Bata radiation.*

#### **6. Gamma ray**

Gamma ray is also named gamma radiation symbolized with γ which is an electromagnetic radiation (**Figure 4**) emitting from the radioactive decay of atomic nuclei [3]. This type of radiation is very common.

### **7. Modes of decay**

Different decay reactions of the radionuclides, the mass number A and atomic number Z of nucleus defined as A, Z are presented in **Table 1**. The column

**Figure 4.** *Gamma radiation.*

(daughter nucleus) represents the difference between the produced nucleus and the parent. Thus, (A–2, Z) means that the mass number is two less than before, but the atomic number is the same as before.

#### **8. Decay chain and uranium isotopes**

The daughter nuclide is a result of the radioactive decay of a certain radioactive element. Daughter is stable or may also be radioactive, so the chain still continues to decay. The resulting second and/or third daughter nuclide may be radioactive leading to sequential radiation, so the process known as decay chain. Uranium is very heavy element has 92 atomic number (**Figure 5**).

Half-life (t) means the time required for a given amount of radionuclide to lose 50% of its activity, and can be expressed as the exponential relationship (**Figure 6**) represents the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay and spontaneously changes into other element by

**Mode of decay Participating particles Daughter**

Alpha decay An alpha particle (A = 4, Z = 2) emitted from nucleus (A�4, Z�2) Proton emission A proton ejected from nucleus (A�1, Z�1) Neutron emission A neutron ejected from nucleus (A�1, Z)

Spontaneous fission Nucleus disintegrates into two or more smaller nuclei and

Cluster decay Nucleus emits a specific type of smaller nucleus (A1, Z1)

Electron capture A nucleus captures an orbiting electron and emits a

smaller than, or larger than, an alpha particle

Beta-negative decay A nucleus emits an electron and an antineutrino (A, Z+1)

Double beta decay A nucleus emits two electrons and two antineutrinos (A, Z+2)

neutrino - The daughter nucleus is left in an excited and

A nucleus absorbs two orbital electrons and emits two neutrinos - The daughter nucleus is left in an excited and

A nucleus absorbs one orbital electron, emits one positron

A nucleus emits two positrons and two neutrinos (A, Z�2)

other particles

unstable state

unstable state

Transitions between states of the same nucleus

ray)

and two neutrinos

Gamma decay Excited nucleus releases a high-energy photon (gamma

Internal conversion Excited nucleus transfers energy to an orbital electron and it is ejected from the atom

Two protons ejected from nucleus simultaneously (A�2, Z�2)

A nucleus emits a positron and a neutrino (A, Z�1)

**nucleus**

—

(A�A1, Z�Z1) + (A1, Z1)

(A, Z�1)

(A, Z�2)

(A, Z�2)

(A, Z)

(A, Z)

The best example for the radioactive decay can be illustrating by the uranium decay chain (**Figure 7**) [4]. The natural decay chain of 238U which eventually decays to 210Po emitting alpha with a half-life of 140 days to produce finally a stable isotope

238U ! 234Th ! 234mPa ! 234U ! 230Th ! 226Ra ! 222Rn ! 218Po ! 214Pb

! 214Bi ! 214Po ! 210Pb ! 210Bi ! 210Po ! 206Pb*:*

emitting particles and energy.

*Detailed radioactive decay reaction after [1].*

Decays with emission of nucleons

*Geochemistry of Radioactive Isotopes*

*DOI: http://dx.doi.org/10.5772/intechopen.91616*

Different modes of beta decay

Positron emission, also beta-positive decay

Double electron capture

Double positron emission

**Table 1.**

Electron capture with positron emission

Double proton emission

which is 206Pb.

**123**

Three isotopes are most common of uranium; these are with their relative abundance and half-life (t1/2):



#### **Table 1.**

(daughter nucleus) represents the difference between the produced nucleus and the parent. Thus, (A–2, Z) means that the mass number is two less than before, but the

The daughter nuclide is a result of the radioactive decay of a certain radioactive element. Daughter is stable or may also be radioactive, so the chain still continues to decay. The resulting second and/or third daughter nuclide may be radioactive leading to sequential radiation, so the process known as decay chain. Uranium is

Three isotopes are most common of uranium; these are with their relative

• 238U has relative abundance 99.2739–99.2752% and half-life 4.4683 109 years.

• 235U has relative abundance 0.7198–0.7202% and half-life 703.8 million years.

• 234U has relative abundance 0.0050–0.0059% and half-life 245,500 years.

atomic number is the same as before.

**Figure 4.** *Gamma radiation.*

*Geochemistry*

**122**

abundance and half-life (t1/2):

**8. Decay chain and uranium isotopes**

very heavy element has 92 atomic number (**Figure 5**).

*Detailed radioactive decay reaction after [1].*

Half-life (t) means the time required for a given amount of radionuclide to lose 50% of its activity, and can be expressed as the exponential relationship (**Figure 6**) represents the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay and spontaneously changes into other element by emitting particles and energy.

The best example for the radioactive decay can be illustrating by the uranium decay chain (**Figure 7**) [4]. The natural decay chain of 238U which eventually decays to 210Po emitting alpha with a half-life of 140 days to produce finally a stable isotope which is 206Pb.

238U ! 234Th ! 234mPa ! 234U ! 230Th ! 226Ra ! 222Rn ! 218Po ! 214Pb ! 214Bi ! 214Po ! 210Pb ! 210Bi ! 210Po ! 206Pb*:*

*Configuration of the uranium atom showing the atomic number and mass number.*

**Figure 6.**

*The exponential relationship of half-life with radioactive decay.*

#### **9. Isotope systems in geological dating**

Many isotope systems are mostly given as examples for dating geologic materials (**Table 2**).

It can be done to use this information to date rocks, for example; usually, the amount (N) of an isotope present today, and the amount of a daughter element produced by decay (D\*), see Eqs. (1) and (2).

$$\mathbf{D}^\* = \mathbf{N}\_0 - \mathbf{N} \tag{1}$$

Consequently, it is possible to calculate the age if you have the number of daughter atoms produced by decay (D\*), while the number of parent atoms (N) is known now with should pay attention for the number of daughter atoms that may

14C 14N 5730 y 100 – 70,000 y Organic Material

**Parent Daughter Half-life Range available Lithology type** 238U 206Pb 4.47 b.y >10 m.y Igneous & sometimes

We can simplify our isochron equation somewhat by noting that if x is small [7],

<sup>38</sup>Sr by β decay. The neutron emits an electron to become a proton. For this decay reaction, <sup>λ</sup> = 1.42 � <sup>10</sup>–11/y, t1/2 = 4.8 � <sup>10</sup><sup>10</sup> y, at present, 27.85%

þ … ¼ 1 þ *x* (4)

metamorphic rocks and minerals

*x*2 2! þ *x*3 3! þ *x*4 4!

have been present prior to the start of our clock.

so that (eλt � 1) = λt, when λt is small.

*<sup>e</sup> <sup>x</sup>* <sup>¼</sup> <sup>1</sup> <sup>þ</sup> *<sup>x</sup>* <sup>þ</sup>

**9.1 The Rb/Sr system**

of natural Rb is 87Rb.

87 <sup>37</sup>Rb ! <sup>87</sup>

**125**

**Figure 7.**

**Table 2.**

*Natural radioactive decay series of 238U.*

*Geochemistry of Radioactive Isotopes*

*DOI: http://dx.doi.org/10.5772/intechopen.91616*

235U 207Pb 707 m.y 232Th 208Pb 14 b.y

147Sm 143Nd 106 b.y

*b.y = billion years; m.y = million years; y = year*

40K 40Ar & 40Ca 1.28 b.y >10,000 y 87Rb 87Sr 48 b.y >10 m.y

*Some radioactive elements with their daughters and dating application.*

$$N = N\_0 \ e^{-\lambda t} \tag{2}$$

λ, the decay constant

$$\mathbf{D}^\* = \mathbf{N}\mathbf{e}\lambda\mathbf{t} - \mathbf{N} = \mathbf{N}(\mathbf{e}\lambda\mathbf{t} - \mathbf{1})\tag{3}$$

#### *Geochemistry of Radioactive Isotopes DOI: http://dx.doi.org/10.5772/intechopen.91616*

**Figure 7.** *Natural radioactive decay series of 238U.*


#### **Table 2.**

**9. Isotope systems in geological dating**

*The exponential relationship of half-life with radioactive decay.*

*Configuration of the uranium atom showing the atomic number and mass number.*

produced by decay (D\*), see Eqs. (1) and (2).

λ, the decay constant

(**Table 2**).

**124**

**Figure 6.**

**Figure 5.**

*Geochemistry*

Many isotope systems are mostly given as examples for dating geologic materials

<sup>D</sup><sup>∗</sup> <sup>¼</sup> N0 � <sup>N</sup> (1)

<sup>D</sup><sup>∗</sup> <sup>¼</sup> Neλ<sup>t</sup> � <sup>N</sup> <sup>¼</sup> N eð Þ <sup>λ</sup><sup>t</sup> � <sup>1</sup> (3)

�*λ<sup>t</sup>* (2)

It can be done to use this information to date rocks, for example; usually, the amount (N) of an isotope present today, and the amount of a daughter element

*N* ¼ *N*<sup>0</sup> *e*

*Some radioactive elements with their daughters and dating application.*

Consequently, it is possible to calculate the age if you have the number of daughter atoms produced by decay (D\*), while the number of parent atoms (N) is known now with should pay attention for the number of daughter atoms that may have been present prior to the start of our clock.

#### **9.1 The Rb/Sr system**

We can simplify our isochron equation somewhat by noting that if x is small [7],

$$e^{\mathbf{x}} = \mathbf{1} + \mathbf{x} + \frac{\mathbf{x}^2}{2!} + \frac{\mathbf{x}^3}{3!} + \frac{\mathbf{x}^4}{4!} + \dots \\ = \mathbf{1} + \mathbf{x} \tag{4}$$

so that (eλt � 1) = λt, when λt is small.

87 <sup>37</sup>Rb ! <sup>87</sup> <sup>38</sup>Sr by β decay. The neutron emits an electron to become a proton. For this decay reaction, <sup>λ</sup> = 1.42 � <sup>10</sup>–11/y, t1/2 = 4.8 � <sup>10</sup><sup>10</sup> y, at present, 27.85% of natural Rb is 87Rb.

#### *Geochemistry*

If we use this system to plug into Eq. (3), then

$$\mathbf{^8\mathbf{\bar{r}}\mathbf{\bar{r}}^\* = \mathbf{\bar{r}}\mathbf{\bar{R}b} \ (\mathbf{e\bar{\lambda}t} - \mathbf{1})} \tag{5}$$

ratio than mantle rocks. Thus, it will be expected if the mantle has a 87Sr/86Sr of say 0.7025, melting of the mantle would produce a magma with a 87Sr/86Sr ratio of 0.7025, and all rocks derived from that mantle would have an initial 87Sr/86Sr ratio of 0.7025. On the other hand, if the crust with 87Sr/86Sr of 0.710 melts, then the resulting magma would have 87Sr/86Sr of 0.710 and rocks derived from that magma would have an initial 87Sr/86Sr ratio of 0.710. So, the rock derived from the mantle or crust

Many Pb isotopes are produced from U and Th isotopes. 238U and 235U and 232Th can produce Pb isotopes during their radioactive decay that can be described as follows:

the present ratio of

get two independent dates from the U-Pb system can be written as:

206Pb 204Pb !

207Pb 204Pb !

> 206Pb 204Pb � � t

> 207Pb 204Pb � � t

238U ! <sup>8</sup>4He <sup>þ</sup> 206Pb by <sup>α</sup> decay (12)

235U ! <sup>7</sup>4He <sup>þ</sup> 207Pb (14)

232Th ! 64He <sup>þ</sup> 208Pb (17)

<sup>137</sup>*:*<sup>8</sup> (16)

<sup>e</sup><sup>λ</sup>238t � <sup>1</sup> � � (19)

<sup>e</sup><sup>λ</sup>235t � <sup>1</sup> � � (20)

<sup>¼</sup> <sup>e</sup><sup>λ</sup>238t � <sup>1</sup> � � (21)

<sup>¼</sup> <sup>e</sup><sup>λ</sup>235t � <sup>1</sup> � � (22)

<sup>λ</sup><sup>238</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>551</sup> � <sup>10</sup>�<sup>10</sup>*=*y, t1*<sup>=</sup>*<sup>2</sup> <sup>¼</sup> <sup>4</sup>*:*<sup>47</sup> � 109 <sup>y</sup> (13)

<sup>λ</sup><sup>235</sup> <sup>¼</sup> <sup>9</sup>*:*<sup>849</sup> � <sup>10</sup>�<sup>10</sup>*=*y, t1*<sup>=</sup>*<sup>2</sup> <sup>¼</sup> <sup>0</sup>*:*<sup>707</sup> � <sup>10</sup><sup>9</sup> <sup>y</sup> (15)

<sup>λ</sup><sup>232</sup> <sup>¼</sup> <sup>4</sup>*:*<sup>948</sup> � <sup>10</sup>�<sup>11</sup>*=*y, t1*<sup>=</sup>*<sup>2</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>4</sup> � <sup>10</sup><sup>10</sup> <sup>y</sup> (18)

238U 204Pb !

235U 204Pb !

0

0

235U 238U <sup>¼</sup> <sup>1</sup>

204Pb is a stable non-radiogenic isotope of Pb, the two isochron equations and

0 þ

0 þ

If these two independent dates are concordant, a concordia diagram will show the values of Pb isotopes that would give concordant dates and can plug in t and

> 238U 204Pb � � t

> 235U 204Pb � � t

� 206Pb 204Pb � �

� 207Pb 204Pb � �

0

0

can determine its initial Sr isotopic ratio accordingly.

**9.2 The U, Th, Pb system**

*Geochemistry of Radioactive Isotopes*

*DOI: http://dx.doi.org/10.5772/intechopen.91616*

232Th does not used in dating.

and

and

**127**

206Pb 204Pb !

207Pb 204Pb !

t ¼

t ¼

solve for the be calculated Eqs. (21) and (22) as follows:

¼

¼

206Pb<sup>∗</sup> 238U !

207Pb<sup>∗</sup> 235U !

but,

$${}^{87}\mathbf{S}\mathbf{r}\_{\mathbf{t}} = {}^{87}\mathbf{S}\mathbf{r}\_{0} + {}^{87}\mathbf{S}\mathbf{r}^\* \tag{6}$$

or

$$\mathbf{^8\mathbf{\tilde{S}r}^\*} = \mathbf{^8\mathbf{\tilde{S}r}} = \mathbf{^8\mathbf{\tilde{S}r}} \\ \mathbf{\tilde{S}r}\_0 \tag{7}$$

Plugging this into Eq. (5)

$$\mathbf{^8\mathbf{S}r}\_t = \mathbf{^8\mathbf{S}r}\_0 + \mathbf{^8\mathbf{R}b} \left(\mathbf{e\lambda t} - \mathbf{1}\right) \tag{8}$$

We still do not know 87Sr0, the amount of 87Sr daughter element initially present. To account for this, we first note that there is an isotope of Sr, 86Sr, that is:

1.non-radiogenic (not produced by another radioactive decay process),

2.non-radioactive (does not decay to anything else).

Thus, 86Sr is a stable isotope, and the amount of 86Sr does not change through time. If we divide Eq. (8) through by the amount of 86Sr, then we get

$$
\begin{pmatrix}
\frac{\text{87}\,\text{Sr}}{\text{86}\,\text{Sr}}\\\\
\text{87}\end{pmatrix}\_{\text{t}} = \begin{pmatrix}
\frac{\text{87}\,\text{Sr}}{\text{86}\,\text{Sr}}\\\\
\end{pmatrix}\_{\text{0}} + \begin{pmatrix}
\text{87}\,\text{Rb}\\\\
\text{86}\,\text{Sr}
\end{pmatrix}\_{\text{t}} \begin{pmatrix}
\text{e}^{\text{kt}} - \text{1}\\\\
\end{pmatrix} \tag{9}
$$

This is known as the isochron equation. In case of Sr was isotopically homogeneous, the time (t equal 0). For instance, 87Sr/86Sr was the same in the igneous mineral at the time of crystallization. Typically, rock – forming minerals more may be have a different amount of 87Rb [5], and accordingly, those minerals are ordinary have a different 87Rb/86Sr at the crystallization time. During the natural cooling, the 87Rb in each mineral will decay to 87Sr, and each mineral will have a different 87Rb and 87Sr over time [6].

And simplify to:

$$
\left(\frac{^{87}\text{Sr}}{^{86}\text{Sr}}\right)\_{\text{t}} = \left(\frac{^{87}\text{Sr}}{^{86}\text{Sr}}\right)\_{\text{0}} + \left(\frac{^{87}\text{Rb}}{^{86}\text{Sr}}\right)\_{\text{t}}\text{kt} \tag{10}
$$

Then time (t) can be computed as:

$$\mathbf{t} = \frac{\left(\frac{^{\text{Sr}}\text{Sr}}{^{\text{Sr}}\text{Sr}}\right)\_{\text{t}} - \left(\frac{^{\text{Sr}}\text{Sr}}{^{\text{Sr}}\text{Sr}}\right)\_{0}}{\left(\frac{^{\text{Sr}}\text{Rb}}{^{\text{Sr}}\text{Sr}}\right)\_{\text{t}}\lambda} \tag{11}$$

The initial ratio (87Sr/86Sr)0, is useful to use as a geochemical tracer because Rb distributed unequally through the Earth over time [7]. The amount of Rb in the earth mantle is typically low (<0.1 ppm). The mantle thus has a low 87Rb/86Sr ratio and would not change its 87Sr/86Sr ratio very much with time, whilst the earth crust has higher amounts of Rb (>20 ppm) and therefore start out with a relatively high 87Rb/86Sr ratio. Over time, this results in crustal rocks having a much higher 87Sr/86Sr

#### *Geochemistry of Radioactive Isotopes DOI: http://dx.doi.org/10.5772/intechopen.91616*

ratio than mantle rocks. Thus, it will be expected if the mantle has a 87Sr/86Sr of say 0.7025, melting of the mantle would produce a magma with a 87Sr/86Sr ratio of 0.7025, and all rocks derived from that mantle would have an initial 87Sr/86Sr ratio of 0.7025.

On the other hand, if the crust with 87Sr/86Sr of 0.710 melts, then the resulting magma would have 87Sr/86Sr of 0.710 and rocks derived from that magma would have an initial 87Sr/86Sr ratio of 0.710. So, the rock derived from the mantle or crust can determine its initial Sr isotopic ratio accordingly.

#### **9.2 The U, Th, Pb system**

If we use this system to plug into Eq. (3), then

but,

*Geochemistry*

or

Plugging this into Eq. (5)

And simplify to:

**126**

87Sr <sup>∗</sup> <sup>¼</sup> 87Rb eð Þ <sup>λ</sup><sup>t</sup> � <sup>1</sup> (5)

87Srt <sup>¼</sup> 87Sr0 <sup>þ</sup> 87Sr <sup>∗</sup> (6)

87Sr <sup>∗</sup> <sup>¼</sup> 87Srt � 87Sr0 (7)

87Srt <sup>¼</sup> 87Sr0 <sup>þ</sup> 87Rb eð Þ <sup>λ</sup><sup>t</sup> � <sup>1</sup> (8)

We still do not know 87Sr0, the amount of 87Sr daughter element initially present. To account for this, we first note that there is an isotope of Sr, 86Sr, that is:

Thus, 86Sr is a stable isotope, and the amount of 86Sr does not change through time.

87Rb 86Sr !

t

87Rb 86Sr !

t

<sup>e</sup><sup>λ</sup><sup>t</sup> � <sup>1</sup> � � (9)

λt (10)

(11)

0 þ

87Sr 86Sr !

87Sr 86Sr � � t � 87Sr 86Sr � � 0

0 þ

87Rb 86Sr � � t λ

The initial ratio (87Sr/86Sr)0, is useful to use as a geochemical tracer because Rb distributed unequally through the Earth over time [7]. The amount of Rb in the earth mantle is typically low (<0.1 ppm). The mantle thus has a low 87Rb/86Sr ratio and would not change its 87Sr/86Sr ratio very much with time, whilst the earth crust has higher amounts of Rb (>20 ppm) and therefore start out with a relatively high 87Rb/86Sr ratio. Over time, this results in crustal rocks having a much higher 87Sr/86Sr

This is known as the isochron equation. In case of Sr was isotopically homogeneous, the time (t equal 0). For instance, 87Sr/86Sr was the same in the igneous mineral at the time of crystallization. Typically, rock – forming minerals more may be have a different amount of 87Rb [5], and accordingly, those minerals are ordinary have a different 87Rb/86Sr at the crystallization time. During the natural cooling, the 87Rb in each mineral will decay to 87Sr, and each mineral will have a different 87Rb and 87Sr over time [6].

1.non-radiogenic (not produced by another radioactive decay process),

If we divide Eq. (8) through by the amount of 86Sr, then we get

87Sr 86Sr !

2.non-radioactive (does not decay to anything else).

t ¼

87Sr 86Sr !

Then time (t) can be computed as:

t ¼

t ¼

87Sr 86Sr !

Many Pb isotopes are produced from U and Th isotopes. 238U and 235U and 232Th can produce Pb isotopes during their radioactive decay that can be described as follows:

$$^{238}\text{U} \rightarrow 8^4 \text{He} + ^{206}\text{Pb by a decay} \tag{12}$$

$$\lambda \mathbf{238} = \mathbf{1.551} \times \mathbf{10^{-10}} / \mathbf{y}, \mathbf{t}\_{1/2} = \mathbf{4.47} \times \mathbf{10^9} \text{ y} \tag{13}$$

$$\text{}^{235}\text{U} \rightarrow \text{}^{\prime 4}\text{He} + \text{}^{207}\text{Pb} \tag{14}$$

$$\text{M235} = 9.849 \times 10^{-10} / \text{y}, \text{t}\_{1/2} = 0.707 \times 10^9 \text{ y} \tag{15}$$

$$\text{In the present ratio of } \frac{^{235}\text{U}}{^{238}\text{U}} = \frac{1}{137.8} \tag{16}$$

$$\text{^{232}Th} \rightarrow \text{6}^{4}\text{He} + ^{208}\text{Pb} \tag{17}$$

$$\text{M232} = 4.948 \times 10^{-11} / \text{y}, \text{t}\_{1/2} = 1.4 \times 10^{10} \text{ y} \tag{18}$$

232Th does not used in dating.

204Pb is a stable non-radiogenic isotope of Pb, the two isochron equations and get two independent dates from the U-Pb system can be written as:

$$
\left(\frac{^{206}\text{Pb}}{^{204}\text{Pb}}\right)\_{\text{t}} = \left(\frac{^{206}\text{Pb}}{^{204}\text{Pb}}\right)\_{\text{0}} + \left(\frac{^{238}\text{U}}{^{204}\text{Pb}}\right)\_{\text{0}}\left(\text{e}^{\lambda\_{238}\text{t}} - \text{1}\right)\tag{19}
$$

and

$$
\left(\frac{^{207}\text{Pb}}{^{204}\text{Pb}}\right)\_{\text{t}} = \left(\frac{^{207}\text{Pb}}{^{204}\text{Pb}}\right)\_{\text{0}} + \left(\frac{^{235}\text{U}}{^{204}\text{Pb}}\right)\_{\text{0}}\left(\text{e}^{\lambda\_{29}\text{t}} - \text{1}\right)\tag{20}
$$

If these two independent dates are concordant, a concordia diagram will show the values of Pb isotopes that would give concordant dates and can plug in t and solve for the be calculated Eqs. (21) and (22) as follows:

$$\left(\frac{^{206}\text{Pb}^{\*}}{^{238}\text{U}}\right) = \frac{\left(\frac{^{206}\text{Pb}}{^{204}\text{Pb}}\right)\_{\text{t}} - \left(\frac{^{206}\text{Pb}}{^{204}\text{Pb}}\right)\_{\text{0}}}{\left(\frac{^{238}\text{U}}{^{204}\text{Pb}}\right)\_{\text{t}}} = \left(\text{e}^{\text{\text{\textdegree{\textdegree{\textdegree{\textdegree}{U}}}}} - 1\right) \tag{21}$$

and

$$
\left(\frac{^{207}\text{Pb}^{\*}}{^{235}\text{U}}\right) = \frac{\left(\frac{^{207}\text{Pb}}{^{204}\text{Pb}}\right)\_{\text{t}} - \left(\frac{^{207}\text{Pb}}{^{204}\text{Pb}}\right)\_{\text{0}}}{\left(\frac{^{205}\text{U}}{^{204}\text{Pb}}\right)\_{\text{t}}} = \left(\text{e}^{\lambda\_{235}\text{t}} - \text{1}\right)\tag{22}
$$

The Concordia is particularly useful in dating of zircon, that usually contains a lot U and less amounts of Pb, so we expect it has large amounts of radiogenic Pb that can be produced. Apatite and sphene are the two minerals that are commonly can be used in radiometric dating as well. Zircon from the crystallization time to the present represents a closed system in case no loss or gain of uranium or lead. The age of the zircon can be determined from its position on the Concordia after plotting the 206Pb\*/238U and 207Pb\*/235U ratios on the Concordia diagram. The discordant dates fall out of the Concordia curve.

The both ends of the Discordia intersect are represented by t0, the older and t\*, the younger. Many reasons lead to Pb leakage. Metamorphism for example, could heat the crystal to the point where Pb will become mobile. Another possible reason cause U leakage, where the discordia is represented by the two points that would give two ages �t\* representing the possible metamorphic event and t0 representing the initial crystallization age of the zircon.

The Pb-Pb isochrons can be normally concluded from combining the two isochron Eqs. (19) and (20).

$$
\frac{\left(\frac{^{207}\text{Pb}}{^{204}\text{Pb}}\right)\_{\text{t}} - \left(\frac{^{207}\text{Pb}}{^{204}\text{Pb}}\right)\_{\text{0}}}{\left(\frac{^{206}\text{Pb}}{^{204}\text{Pb}}\right)\_{\text{t}} - \left(\frac{^{235}\text{U}}{^{204}\text{Pb}}\right)\_{\text{0}}} = \left(\frac{^{235}\text{U}}{^{238}\text{U}}\right) \left[\frac{\left(\text{e}^{\lambda\text{sat}} - \mathbf{1}\right)}{\left(\text{e}^{\lambda\text{sat}} - \mathbf{1}\right)}\right] \tag{23}
$$

$$\frac{^{238}\text{U}}{^{238}\text{U}} = \frac{1}{137.8} \tag{24}$$

This age represents the maximum age of the Earth. From the Pb-Pb isochron Eq. (23) and based on meteorites that may have been formed at the same time the solar system in which basically the Earth formed as well. The thing to be needed to date meteorites is knowing the initial ratios of the Pb isotopes. Two major types of meteorites are recognized; Fe- meteorites and stony (or chondritic) meteorites. The Fe-meteorites contain troilite (FeS) that has no U. Since the mineral troilite contains no U, all of the Pb present in the troilite is the Pb originally present, and none of it has been produced by U decay. Thus, the troilite in the Fe-meteorites will provide

The Pb ratios can be determined in other meteorites and check if they fall on the isochron of Pb-Pb that passes through the initial ratios determined from troilite in Fe-meteorites. The slope of this isochron (Geochron) estimated the earth age is of 4.55 � 0.07 � <sup>10</sup><sup>9</sup> yr. Consequently, the best estimation of the age of the Earth is

147Sm decays to 143Nd by alpha decay with half-life of 106 � 2 b.y. [8], 147Sm,

The isochron equation is described based on whether the 144Nd is stable and

0 þ

In the nature, 40K makes up 0.119% of natural K, as it is a radioactive element,

The equation above is not used, because 40Ca can be present as both radiogenic

The age of the rock can be estimated later from the isochron equation that basically can be drawn by the determination of the 143Nd/144Nd and 147Sm/144Nd

143Nd 144Nd !

147Sm ! 143Nd (29)

<sup>λ</sup> <sup>¼</sup> <sup>6</sup>*:*<sup>54</sup> � <sup>10</sup>–<sup>12</sup>*=*yr, t1*<sup>=</sup>*<sup>2</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>06</sup> � <sup>10</sup><sup>11</sup> <sup>y</sup> (30)

147Sm 144Nd !

t

40K ! 40Ca by <sup>β</sup> decay (32)

40K ! 40Ar by electron capture (33)

<sup>λ</sup> <sup>¼</sup> <sup>5</sup>*:*<sup>305</sup> � <sup>10</sup>–<sup>10</sup>*=*y, t1*<sup>=</sup>*<sup>2</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>31</sup> � <sup>10</sup><sup>9</sup> <sup>y</sup> (34)

<sup>λ</sup><sup>e</sup> <sup>¼</sup> <sup>0</sup>*:*<sup>585</sup> � <sup>10</sup>–<sup>10</sup>*=*<sup>y</sup> (35)

<sup>e</sup><sup>λ</sup><sup>t</sup> � <sup>1</sup> � � (31)

148Sm, 149Sm, and 144Nd are radioactive, three nuclides accordingly generated 144Nd, 145Nd, and 140Ce [9].

with the initial ratios of 206Pb/204Pb and 207Pb/204Pb.

143Nd 144Nd !

its decay can be presented as follows [10]:

t ¼

4.55 billion years.

*Geochemistry of Radioactive Isotopes*

*DOI: http://dx.doi.org/10.5772/intechopen.91616*

**10.1 Sm-Nd dating**

non-radiogenic as:

**10.2 K-Ar dating**

**129**

ratios for several minerals.

and non-radiogenic Ca [10].

For the combined process,

and for the Ar branch of the decay scheme

Then, and by assuming that the 206Pb and 207Pb dates are the same, then Eq. (23) is the equation have a slope.

$$\mathbf{m} = \frac{1}{\mathbf{1} \mathbf{3} \mathbf{7}.88} \left[ \frac{(\mathbf{e}^{\lambda\_{238}} - \mathbf{1})}{(\mathbf{e}^{\lambda\_{238}} - \mathbf{1})} \right] \tag{25}$$

that passes through the point.

$$
\begin{pmatrix}
\frac{^{207}\text{Pb}}{^{204}\text{Pb}} \end{pmatrix}\_{\text{0},} \begin{pmatrix}
\frac{^{206}\text{Pb}}{^{204}\text{Pb}} \end{pmatrix}\_{\text{0}} \tag{26}
$$

#### **10. The age of the earth and dating**

The oldest rock found in Canada, with an age of 3.962 b.y �3 m.y. This provide only a minimum age of the Earth. The age of the earth can be computed based on the chemical concept that is the 235U/238U ratio may have been 1.0 when the elements formed. So, from:

$$\mathbf{N} = \mathbf{N}\_0 \mathbf{e}^{-\lambda t} \tag{27}$$

the

$$\frac{^{238}\text{U}}{^{238}\text{U}} = \frac{^{235}\text{U}\_0\text{e}^{-\lambda\_{238}\text{t}}}{^{238}\text{U}\_0\text{e}^{-\lambda\_{238}\text{t}}}\tag{28}$$

Finally, t is about 6 b.y.

*Geochemistry of Radioactive Isotopes DOI: http://dx.doi.org/10.5772/intechopen.91616*

This age represents the maximum age of the Earth. From the Pb-Pb isochron Eq. (23) and based on meteorites that may have been formed at the same time the solar system in which basically the Earth formed as well. The thing to be needed to date meteorites is knowing the initial ratios of the Pb isotopes. Two major types of meteorites are recognized; Fe- meteorites and stony (or chondritic) meteorites. The Fe-meteorites contain troilite (FeS) that has no U. Since the mineral troilite contains no U, all of the Pb present in the troilite is the Pb originally present, and none of it has been produced by U decay. Thus, the troilite in the Fe-meteorites will provide with the initial ratios of 206Pb/204Pb and 207Pb/204Pb.

The Pb ratios can be determined in other meteorites and check if they fall on the isochron of Pb-Pb that passes through the initial ratios determined from troilite in Fe-meteorites. The slope of this isochron (Geochron) estimated the earth age is of 4.55 � 0.07 � <sup>10</sup><sup>9</sup> yr. Consequently, the best estimation of the age of the Earth is 4.55 billion years.

#### **10.1 Sm-Nd dating**

The Concordia is particularly useful in dating of zircon, that usually contains a lot U and less amounts of Pb, so we expect it has large amounts of radiogenic Pb that can be produced. Apatite and sphene are the two minerals that are commonly can be used in radiometric dating as well. Zircon from the crystallization time to the present represents a closed system in case no loss or gain of uranium or lead. The age of the zircon can be determined from its position on the Concordia after plotting the 206Pb\*/238U and 207Pb\*/235U ratios on the Concordia diagram. The

The both ends of the Discordia intersect are represented by t0, the older and t\*, the younger. Many reasons lead to Pb leakage. Metamorphism for example, could heat the crystal to the point where Pb will become mobile. Another possible reason cause U leakage, where the discordia is represented by the two points that would give two ages �t\* representing the possible metamorphic event and t0 representing

The Pb-Pb isochrons can be normally concluded from combining the two

0

235U 238U

Then, and by assuming that the 206Pb and 207Pb dates are the same, then Eq. (23)

<sup>e</sup><sup>λ</sup>238t � <sup>1</sup> � � eð Þ <sup>λ</sup>235t � 1 � �

206Pb 204Pb !

0

<sup>N</sup> <sup>¼</sup> N0e�λ<sup>t</sup> (27)

238U0e�λ238t (28)

� � <sup>e</sup><sup>λ</sup>235t � <sup>1</sup> � �

eð Þ <sup>λ</sup>238t � 1 � �

<sup>137</sup>*:*<sup>8</sup> (24)

(23)

(25)

(26)

0 ¼

235U 238U <sup>¼</sup> <sup>1</sup>

discordant dates fall out of the Concordia curve.

the initial crystallization age of the zircon.

207Pb 204Pb � �

206Pb 204Pb � �

t

t

� 207Pb 204Pb � �

� 206Pb 204Pb � �

<sup>m</sup> <sup>¼</sup> <sup>1</sup> 137*:*88

> 207Pb 204Pb !

> > 235U 238U <sup>¼</sup>

0,

The oldest rock found in Canada, with an age of 3.962 b.y �3 m.y. This provide only a minimum age of the Earth. The age of the earth can be computed based on the chemical concept that is the 235U/238U ratio may have been 1.0 when the

235U0e�λ235t

isochron Eqs. (19) and (20).

*Geochemistry*

is the equation have a slope.

that passes through the point.

**10. The age of the earth and dating**

elements formed. So, from:

Finally, t is about 6 b.y.

the

**128**

147Sm decays to 143Nd by alpha decay with half-life of 106 � 2 b.y. [8], 147Sm, 148Sm, 149Sm, and 144Nd are radioactive, three nuclides accordingly generated 144Nd, 145Nd, and 140Ce [9].

$$^{147}\text{Sm} \to \,^{143}\text{Nd} \tag{29}$$

$$
\lambda = 6.54 \times 10^{-12} / \text{yr}, \mathbf{t}\_{1/2} = 1.06 \times 10^{11} \text{ y} \tag{30}
$$

The isochron equation is described based on whether the 144Nd is stable and non-radiogenic as:

$$
\left(\frac{^{143}\text{Nd}}{^{144}\text{Nd}}\right)\_{\text{t}} = \left(\frac{^{143}\text{Nd}}{^{144}\text{Nd}}\right)\_{\text{0}} + \left(\frac{^{147}\text{Sm}}{^{144}\text{Nd}}\right)\_{\text{t}}\left(\text{e}^{\lambda\text{t}} - \text{1}\right)\tag{31}
$$

The age of the rock can be estimated later from the isochron equation that basically can be drawn by the determination of the 143Nd/144Nd and 147Sm/144Nd ratios for several minerals.

#### **10.2 K-Ar dating**

In the nature, 40K makes up 0.119% of natural K, as it is a radioactive element, its decay can be presented as follows [10]:

$$^{40}\text{K} \rightarrow \, ^{40}\text{Ca by } \emptyset \text{ decay} \tag{32}$$

The equation above is not used, because 40Ca can be present as both radiogenic and non-radiogenic Ca [10].

$$^{40}\text{K} \rightarrow \, ^{40}\text{Ar by electron capture} \tag{33}$$

For the combined process,

$$
\lambda = \text{5.305} \times \text{10}^{-10} / \text{y}, \text{t}\_{1/2} = \text{1.31} \times \text{10}^9 \text{ y} \tag{34}
$$

and for the Ar branch of the decay scheme

$$
\lambda \mathbf{e} = \mathbf{0}.\mathbf{585} \times \mathbf{10^{-10}/y} \tag{35}
$$

Argon is a gas easily can escape from a magma or liquid, therefore, the percentage of initial 40Ar is expressed as zero; during the rapid cooling of magma, quanitity of the Ar may be trapped. The date consequently obtained will be older than the date at which the magma erupted.

The dating equation used for K-Ar is:

$$\mathbf{^{40}Ar} = \frac{\lambda\_{\text{e}}}{\lambda} \mathbf{^{40}K} (\mathbf{e^{\lambda t}} - \mathbf{1}) \tag{36}$$

**11. Discussion and conclusions**

*DOI: http://dx.doi.org/10.5772/intechopen.91616*

*Geochemistry of Radioactive Isotopes*

dating marine shale containing coal.

**131**

This chapter deals with the various types of radiation emitted by radioactive nuclides with principles of radionuclide decay and its radiations. Here an overview of some of the many dating radioactive techniques that play as significant role in our day-to-day lives. The dating techniques developed for defining reliable ages of geologic events other geochronological studies are recording of the isotope concentrations. All radiometric clocks depend on a radioactive "parent" isotope that decays to a daughter stable isotope of another element at a constant rate on geologic timescales. This process may take single step, or it may involve many stages of decay products before reaching the final stable daughter isotope. The half-life of the initial quantity of parent isotope to decay must be on the same order of magnitude as the time span to be measured. The Concordia–Discordia model has been developed for the U and Pb isotopes. The 235U transforms to 207Pb through a chain of radioactive nuclides, releasing (235–207)/4 = 7α-particles with the constant <sup>λ</sup>5 = 9.8<sup>10</sup>–10. The 238U turns to 206Pb releasing (238–206)/4 = 8α-particles with the constant <sup>λ</sup>8 = 1.55 <sup>10</sup>–10 [16]. Currently, the ratio of 238U/235U (137.88) is growing. Both isotopes of uranium are closely connected to each other in kinetic processes due to the value √238/235 = 1.0063, which is close to 1. The Discordant values can be obtained from the development of the Concordia–Discordia model as an open system with losses of radiogenic lead in accessory minerals such as zircon, monazite, apatite etc. [17]. A very wide time range, not only the 12 b.y. of the Universe age and the 4.5 b.y. of the Earth's age can be explore, but also the details related paleontology through the history of the Earth and recent events of the last millennia [12]. The K-Ar dating technique developed soon after the discovery of 40K and provided an important dating tool beside U-Pb and U-He dating methods. The half-life (1250 m.y) made this method is most popular for dating geological events [18]. The K-Ar dating are based on the decay of a 40K to an isotope of 40Ar by a branching process; 10.48% of 40K decays to 40Ar by β + decay, and 89.52% decays to 40Ca by β- to the ground state [10]. The age measured by K-Ar techniques reflects the time since radiogenic argon produced by decay of 40K, became trapped in the mineral or rock. The radiogenic noble gas daughter nuclides provide many methods for determining not only the chronology of events but also thermal histories combined with U-Pb and Rb-Sr dating techniques. This technique uses to conclude the cooling history based on use mineral closure or field estimates [19]. It can be applied for dating young volcanic eruptions and for low-temperature phases such as clay minerals like illite. In addition, they can be used for exploring. Despite the Rhenium–osmium (Re-Os), an applicable method was first applied to meteorites [15]; it also provides a chronometer for directly dating both of sulfides and oxides ore minerals. Recently, this technique is developed and become capable to estimate dating via dealing with very low content of Re and Os. The relative abundance of Osmium is the earth's core and extraterrestrial material with a very leaser amount (ppt) in the mantle and it can be stored in sulfide and oxide minerals in the crust. It 8is best method for dating the age of gold in auriferous pyrites, it also used for

It is difficult to obtain good precision and accuracy for radiocarbon due to its abundancy in the environment and it is possible to contaminate from material of a different age. Consequently, the methods for radiocarbon measuring are well tested, reproduced and carefully controlled under specific lab conditions. Recently, the radiocarbon methods have been developed, over the last 30 years to cover most of the materials suitable for radiocarbon measurement. The AMS system at Oxford was built with very high precision and accuracy for radiocarbon dating by High Voltage Engineering Europa BV. For high precious in situ age dating of Pb-U, Hf

where <sup>λ</sup><sup>e</sup> <sup>λ</sup> <sup>¼</sup> <sup>0</sup>*:*11 and refers to fraction of 40K that decays to 40Ar.

Many points need to have attention when use K-Ar dating, the use of minerals like sanidine or biotite is better to use whole rocks because minerals not contain excess Ar. Other thing, some atmospheric argon originated from volcanic eruptions could be absorbed onto the sample surface, 40Ar should be corrected for accordingly. Additionally, most minerals lose Ar during metamorphism due to high temperature, so the date will represent the metamorphic event (**Table 3**).

#### **10.3 14C dating**

Radiocarbon dating is different than the other methods of dating because it cannot be used to directly date rocks, but can only be used to date organic material produced by once living organisms [12]. Radiocarbon (14C) has a short half-life (5730 y), it is therefore only used to date materials younger than about 70,000 years. The ratio of 14C to 14N in the Earth's atmosphere is constant and the organism have the same ratio of 14C to 14N as the atmosphere. When an organism dies, the 14C decays back to 14N, with a half-life of 5730 years. Measuring the amount of 14C in this dead material thus enables the determination of the time elapsed since the organism died. Bones, teeth, charcoal, fossilized wood, and shells are materials can be used for dating.

#### **10.4 Re-Os dating**

Rhenium has stable 185Re and the radioactive 187Re. The latter is the most abundant (62.6%) and decays to 187Os based on beta decay, typically with a half-life of 41.6 � 109 y [13]. Osmium has seven isotopes; only two are the product of natural decay of radioactive isotopes: 186Os is produced from 190Pt by α-decay (half-life 4.7 � 1011 y, [14]) and 187Os by <sup>β</sup>-decay of 187Re. The two radiogenic isotopes 187Os (�2%) and 186Os (�1.6%) are typically normalized to the stable 188Os (13.24%). Rhenium-osmium (Re-Os), an applicable method was first applied to meteorites [15]; it provides a chronometer for directly dating both of sulfides and oxides ore minerals.


**Table 3.**

*Decay constants for K-Ar and Ar-Ar dating [11].*

#### **11. Discussion and conclusions**

Argon is a gas easily can escape from a magma or liquid, therefore, the percentage of initial 40Ar is expressed as zero; during the rapid cooling of magma, quanitity of the Ar may be trapped. The date consequently obtained will be older than the

40K eλ<sup>t</sup> � <sup>1</sup> (36)

40Ar <sup>¼</sup> <sup>λ</sup><sup>e</sup> λ

<sup>λ</sup> <sup>¼</sup> <sup>0</sup>*:*11 and refers to fraction of 40K that decays to 40Ar. Many points need to have attention when use K-Ar dating, the use of minerals like sanidine or biotite is better to use whole rocks because minerals not contain excess Ar. Other thing, some atmospheric argon originated from volcanic eruptions could be absorbed onto the sample surface, 40Ar should be corrected for accordingly. Additionally, most minerals lose Ar during metamorphism due to high temperature, so the date will represent the metamorphic event (**Table 3**).

Radiocarbon dating is different than the other methods of dating because it cannot be used to directly date rocks, but can only be used to date organic material produced by once living organisms [12]. Radiocarbon (14C) has a short half-life

70,000 years. The ratio of 14C to 14N in the Earth's atmosphere is constant and the organism have the same ratio of 14C to 14N as the atmosphere. When an organism dies, the 14C decays back to 14N, with a half-life of 5730 years. Measuring the amount of 14C in this dead material thus enables the determination of the time elapsed since the organism died. Bones, teeth, charcoal, fossilized wood, and shells

Rhenium has stable 185Re and the radioactive 187Re. The latter is the most abundant (62.6%) and decays to 187Os based on beta decay, typically with a half-life of 41.6 � 109 y [13]. Osmium has seven isotopes; only two are the product of natural decay of radioactive isotopes: 186Os is produced from 190Pt by α-decay (half-life 4.7 � 1011 y, [14]) and 187Os by <sup>β</sup>-decay of 187Re. The two radiogenic isotopes 187Os (�2%) and 186Os (�1.6%) are typically normalized to the stable 188Os (13.24%). Rhenium-osmium (Re-Os), an applicable method was first applied to meteorites [15]; it provides a chronometer for directly dating both of sulfides and oxides ore

**Decay Decay factor value** 40K ! 40Ca by <sup>β</sup>- λβ- 4.962 � <sup>10</sup>�<sup>10</sup> <sup>a</sup>�<sup>1</sup> 40K ! 40Ar by electron capture and γ λ<sup>e</sup> 0.572 � <sup>10</sup>�<sup>10</sup> <sup>a</sup>�<sup>1</sup> 40K ! 40Ar by electron capture <sup>λ</sup>' <sup>e</sup> 0.0088 � <sup>10</sup>�<sup>10</sup> <sup>a</sup>�<sup>1</sup> combined value <sup>λ</sup> <sup>=</sup> λβ- + <sup>λ</sup>ec + <sup>λ</sup>' ec 5.543 � <sup>10</sup>�<sup>10</sup> <sup>a</sup>�<sup>1</sup>

present day 40K/K 0.0001167

(5730 y), it is therefore only used to date materials younger than about

date at which the magma erupted.

are materials can be used for dating.

*Decay constants for K-Ar and Ar-Ar dating [11].*

where <sup>λ</sup><sup>e</sup>

*Geochemistry*

**10.3 14C dating**

**10.4 Re-Os dating**

minerals.

**Table 3.**

**130**

The dating equation used for K-Ar is:

This chapter deals with the various types of radiation emitted by radioactive nuclides with principles of radionuclide decay and its radiations. Here an overview of some of the many dating radioactive techniques that play as significant role in our day-to-day lives. The dating techniques developed for defining reliable ages of geologic events other geochronological studies are recording of the isotope concentrations. All radiometric clocks depend on a radioactive "parent" isotope that decays to a daughter stable isotope of another element at a constant rate on geologic timescales. This process may take single step, or it may involve many stages of decay products before reaching the final stable daughter isotope. The half-life of the initial quantity of parent isotope to decay must be on the same order of magnitude as the time span to be measured. The Concordia–Discordia model has been developed for the U and Pb isotopes. The 235U transforms to 207Pb through a chain of radioactive nuclides, releasing (235–207)/4 = 7α-particles with the constant <sup>λ</sup>5 = 9.8<sup>10</sup>–10. The 238U turns to 206Pb releasing (238–206)/4 = 8α-particles with the constant <sup>λ</sup>8 = 1.55 <sup>10</sup>–10 [16]. Currently, the ratio of 238U/235U (137.88) is growing. Both isotopes of uranium are closely connected to each other in kinetic processes due to the value √238/235 = 1.0063, which is close to 1. The Discordant values can be obtained from the development of the Concordia–Discordia model as an open system with losses of radiogenic lead in accessory minerals such as zircon, monazite, apatite etc. [17]. A very wide time range, not only the 12 b.y. of the Universe age and the 4.5 b.y. of the Earth's age can be explore, but also the details related paleontology through the history of the Earth and recent events of the last millennia [12]. The K-Ar dating technique developed soon after the discovery of 40K and provided an important dating tool beside U-Pb and U-He dating methods. The half-life (1250 m.y) made this method is most popular for dating geological events [18]. The K-Ar dating are based on the decay of a 40K to an isotope of 40Ar by a branching process; 10.48% of 40K decays to 40Ar by β + decay, and 89.52% decays to 40Ca by β- to the ground state [10]. The age measured by K-Ar techniques reflects the time since radiogenic argon produced by decay of 40K, became trapped in the mineral or rock. The radiogenic noble gas daughter nuclides provide many methods for determining not only the chronology of events but also thermal histories combined with U-Pb and Rb-Sr dating techniques. This technique uses to conclude the cooling history based on use mineral closure or field estimates [19]. It can be applied for dating young volcanic eruptions and for low-temperature phases such as clay minerals like illite. In addition, they can be used for exploring. Despite the Rhenium–osmium (Re-Os), an applicable method was first applied to meteorites [15]; it also provides a chronometer for directly dating both of sulfides and oxides ore minerals. Recently, this technique is developed and become capable to estimate dating via dealing with very low content of Re and Os. The relative abundance of Osmium is the earth's core and extraterrestrial material with a very leaser amount (ppt) in the mantle and it can be stored in sulfide and oxide minerals in the crust. It 8is best method for dating the age of gold in auriferous pyrites, it also used for dating marine shale containing coal.

It is difficult to obtain good precision and accuracy for radiocarbon due to its abundancy in the environment and it is possible to contaminate from material of a different age. Consequently, the methods for radiocarbon measuring are well tested, reproduced and carefully controlled under specific lab conditions. Recently, the radiocarbon methods have been developed, over the last 30 years to cover most of the materials suitable for radiocarbon measurement. The AMS system at Oxford was built with very high precision and accuracy for radiocarbon dating by High Voltage Engineering Europa BV. For high precious in situ age dating of Pb-U, Hf

and U-Th isotope ratios in very small minerals like zircons, it is recommended to use the Thermo Scientific Neptune XT MC-ICP-MS or Thermo Scientific Element 2 and Thermo Scientific Element XR High-Resolution ICP-MS, combined with a laser ablation system. The Thermo Scientific Triton XT Multicollector Thermal Ionization Mass Spectrometer (TIMS), provides the ultimate precision for U-Pb geochronology, while The Triton XT TIMS is an equipment with high-quality age dating for Rb-Sr, Sm-Nd and Re-Os.

Where the 87Sr1 is the number of the initial 87Sr atoms. The given nuclides are of so difficult to measure their absolute abundance, so, it is suitable to find isotope ratio by dividing by 86Sr which is not radiogenic and accordingly still constant with

> I þ 87Rb 86Sr

Currently, strontium isotope ratio (p) can be measured by mass spectrometry,

87Sr 86Sr !

Over geological time, Rb-rich minerals "like lepidolite" develop ratio (0.712) of 87Rb/86Sr and may use in chronological studies without error. The Rb-Sr method was extended to include other mineral such as mica (biotite and muscovite) as well as potash feldspar that have lower Rb/Sr ratios. The discordant dates are suggested based on the initial ration (0.712) when the real initial ratio was higher. This expressed as a problem and was overcome by the isochron diagram designed by [24] who developed a new way for treating Rb-Sr data based on the principle of

In this way, 87Sr/86Sr (*y*) is plotted versus 87Rb/86Sr (*x*), then the intercept *c* is

This figure presents a suite of co-magmatic minerals of same age and initial of 87Sr/86Sr ratio, forming a line called isochron. From slop of isochron, *<sup>m</sup>* <sup>¼</sup> *<sup>e</sup>*λ*<sup>t</sup>* � 1, the mineral age can be determined. The mineral with very low Pb may yield the

p �

86Sr 87Sr !

I

y ¼ c þ xm (40)

3 5

9 = ;

(39)

<sup>e</sup><sup>λ</sup><sup>t</sup> � <sup>1</sup> � � (38)

87Sr 86Sr !

and the 87Rb/86Sr is calculated from Rb/Sr weigh ratio. From the initial ratio

2 4

86Sr 87Rb

87Sr 86Sr !

87Rb/86Sr)I estimated, time (t) can be computed as:

ln 1 þ

*Schematic Rb-Sr isochron diagram for a suit of co-magmatic igneous minerals [25].*

8 < :

<sup>t</sup> <sup>¼</sup> <sup>1</sup> λ

the initial 87Sr/86Sr ratio (**Figure 8**).

p ¼

time as follows:

*Geochemistry of Radioactive Isotopes*

*DOI: http://dx.doi.org/10.5772/intechopen.91616*

linear equation:

**Figure 8.**

**133**

(

To be useful, result must be accurate, so uncertainty must always be taken into account. The geochronological result is influenced by uncertainty. So, if it does not be known well, result is scientifically meaningless. The uncertainty is coming from error in sampling, laboratory procedure; adaption of methods to the problem in question [12]. Overall, the source of uncertainty obtained from:


#### **11.1 Analytical methods**

The radiogenic isotopes are typically separated from the no-radiogenic isotopes using spectrometer whenever they used as dating tools or tracers. Sample is ionized normally in thermal-ionization mass spectrometer (TIMS). Recently, the induced coupled plasma (ICP) is technique used for the chemical purification before mass spectrometry method. The laser ablation is also used for analyzing mineral with high concentration of radiogenic elements. However, in samples of whole-rocks, in which the concentration of radiogenic isotope is mostly low, it is necessary to preconcentrate after dissolution and chemical extraction. The silicate geological samples are routinely dissolved in hot method using either concentrated HF acid or HCLO4 acid at atmospheric pressure; so, the most rock-forming minerals are dissolved, but the resistant minerals like zircon must be dissolved under pressure in a bomb at 220°C. The bomb liner and beaker are made of poly-fluorinated ethylene [20]. The formation of fluoride is the most common problem that may encounter after dissolution in HF as an insoluble in HCl acid. Consequently, the refluxing with HNO3 is needed [21]. The additional adding of HNO3 before completely evaporation of HF leads to promote process [22]. If at some stage, complete digestion is not achieved, decant off the solution is recommended and return to undissolved fraction at the previous stage for a second acid attack [23]. Thereafter, the solution rich in isotope is split for isotopedilution analysis and for accurate-isotope ratio analysis.

#### **11.2 Dating of igneous rocks**

#### *11.2.1 Sr-model ages*

The Rb-Sr is used widely as a method provides a great information of igneous rock dating. The naturel process begins from the decay of 87Rb occurred in minerals to 87Sr, so the number of 87Sr daughters produced informs us about t years ago:

$${}^{87}\text{Sr} = {}^{87}\text{Sr}\_1 + {}^{87}\text{Rb} \left( \mathbf{e}^{\lambda t} \, \mathbf{l} - \mathbf{1} \right) \tag{37}$$

*Geochemistry of Radioactive Isotopes DOI: http://dx.doi.org/10.5772/intechopen.91616*

and U-Th isotope ratios in very small minerals like zircons, it is recommended to use the Thermo Scientific Neptune XT MC-ICP-MS or Thermo Scientific Element 2 and Thermo Scientific Element XR High-Resolution ICP-MS, combined with a laser ablation system. The Thermo Scientific Triton XT Multicollector Thermal Ionization Mass Spectrometer (TIMS), provides the ultimate precision for U-Pb geochronology, while The Triton XT TIMS is an equipment with high-quality age dating for

To be useful, result must be accurate, so uncertainty must always be taken into account. The geochronological result is influenced by uncertainty. So, if it does not be known well, result is scientifically meaningless. The uncertainty is coming from error in sampling, laboratory procedure; adaption of methods to the problem in

The radiogenic isotopes are typically separated from the no-radiogenic isotopes using spectrometer whenever they used as dating tools or tracers. Sample is ionized normally in thermal-ionization mass spectrometer (TIMS). Recently, the induced coupled plasma (ICP) is technique used for the chemical purification before mass spectrometry method. The laser ablation is also used for analyzing mineral with high concentration of radiogenic elements. However, in samples of whole-rocks, in which

the concentration of radiogenic isotope is mostly low, it is necessary to pre-

concentrate after dissolution and chemical extraction. The silicate geological samples are routinely dissolved in hot method using either concentrated HF acid or HCLO4 acid at atmospheric pressure; so, the most rock-forming minerals are dissolved, but the resistant minerals like zircon must be dissolved under pressure in a bomb at 220°C. The bomb liner and beaker are made of poly-fluorinated ethylene [20]. The formation of fluoride is the most common problem that may encounter after dissolution in HF as an insoluble in HCl acid. Consequently, the refluxing with HNO3 is needed [21]. The additional adding of HNO3 before completely evaporation of HF leads to promote process [22]. If at some stage, complete digestion is not achieved, decant off the solution is recommended and return to undissolved fraction at the previous stage for a second acid attack [23]. Thereafter, the solution rich in isotope is split for isotope-

The Rb-Sr is used widely as a method provides a great information of igneous rock dating. The naturel process begins from the decay of 87Rb occurred in minerals to 87Sr, so the number of 87Sr daughters produced informs us about t years ago:

87Sr <sup>¼</sup> 87Sr1 <sup>þ</sup> 87Rb eλ<sup>t</sup> � <sup>1</sup> (37)

question [12]. Overall, the source of uncertainty obtained from:

Rb-Sr, Sm-Nd and Re-Os.

*Geochemistry*

a. collecting samples

d. Age calculations

**11.1 Analytical methods**

b. Parent decay methods

c. Long half-life parent daughter methods

dilution analysis and for accurate-isotope ratio analysis.

**11.2 Dating of igneous rocks**

*11.2.1 Sr-model ages*

**132**

Where the 87Sr1 is the number of the initial 87Sr atoms. The given nuclides are of so difficult to measure their absolute abundance, so, it is suitable to find isotope ratio by dividing by 86Sr which is not radiogenic and accordingly still constant with time as follows:

$$
\left(\frac{^{87}\text{Sr}}{^{86}\text{Sr}}\right)\_{\text{p}} = \left(\frac{^{87}\text{Sr}}{^{86}\text{Sr}}\right)\_{\text{l}} + \frac{^{87}\text{Rb}}{^{86}\text{Sr}}\left(\text{e}^{\lambda t} - \text{1}\right)\tag{38}
$$

Currently, strontium isotope ratio (p) can be measured by mass spectrometry, and the 87Rb/86Sr is calculated from Rb/Sr weigh ratio. From the initial ratio ( 87Rb/86Sr)I estimated, time (t) can be computed as:

$$\mathbf{t} = \frac{\mathbf{1}}{\lambda} \ln \left\{ \mathbf{1} + \frac{^{86}\mathbf{Sr}}{^{87}\mathbf{Rb}} \left[ \left( \frac{^{87}\mathbf{Sr}}{^{86}\mathbf{Sr}} \right)\_{\mathbf{P}} - \left( \frac{^{86}\mathbf{Sr}}{^{87}\mathbf{Sr}} \right)\_{\mathbf{I}} \right] \right\} \tag{39}$$

Over geological time, Rb-rich minerals "like lepidolite" develop ratio (0.712) of 87Rb/86Sr and may use in chronological studies without error. The Rb-Sr method was extended to include other mineral such as mica (biotite and muscovite) as well as potash feldspar that have lower Rb/Sr ratios. The discordant dates are suggested based on the initial ration (0.712) when the real initial ratio was higher. This expressed as a problem and was overcome by the isochron diagram designed by [24] who developed a new way for treating Rb-Sr data based on the principle of linear equation:

$$\mathbf{y} = \mathbf{c} + \mathbf{x}\mathbf{m} \tag{40}$$

In this way, 87Sr/86Sr (*y*) is plotted versus 87Rb/86Sr (*x*), then the intercept *c* is the initial 87Sr/86Sr ratio (**Figure 8**).

This figure presents a suite of co-magmatic minerals of same age and initial of 87Sr/86Sr ratio, forming a line called isochron. From slop of isochron, *<sup>m</sup>* <sup>¼</sup> *<sup>e</sup>*λ*<sup>t</sup>* � 1, the mineral age can be determined. The mineral with very low Pb may yield the

**Figure 8.** *Schematic Rb-Sr isochron diagram for a suit of co-magmatic igneous minerals [25].*

#### **Figure 9.**

*Rb-Sr isochron diagram on axis of equal magnitude showing production of 87Sr as 87Rb is consumed in two hypothetical samples [25].*

initial ratio directly on y-axis. On **Figure 9**, the 87Sr/86Sr increase with decrease 87Rb/86Sr due to decay Rb over time. The slope of ischron is increased accordingly with time. Practically, the *y*-axis is expanded much to displays rocks of geological time clearly, and the growth lines become vertical accordingly.

#### **11.3 Erupted isochro**

The original isotopic composition of mantle is basically inherited in the primary basic magma. The alkali ocean-island basalts were investigated for the Rb-Sr system [26]. The results of fourteen wide range type of ocean- island basalt samples plotted on an isochron displayed a proportional correlation to a slop age of about 2B.y representing the time of mantle isolation [25]. This age is known as a mantle isochrones that is also extended to continental igneous rocks [27]. The ratio of 87Sr/86Sr should correct back to initial ratio at the time of magmatism before plotting versus 87Rb/86Sr, so these are termed as pesud-oisochrons. Data of plotting 30 samples from both volcanic and plutonic continental igneous rock suits formed a roughly linear array. The pesud-oisochrons generates from two lines representing crustal contamination of mantle-derived basaltic magma, Scientist replaced that by timing the mantle differentiation events that established mantle domains of different ratio of Rb/Sr in subcontinental lithosphere. This suggestion does not provide reliable results to ascribe age significantly to erupted isochrones. However, the only isotopeisotope mantle isochrones is reliable and can be interpreted and used significantly as tool for dating the age of mantle differentiation events.

**Author details**

**135**

Salih Muhammad Awadh

*Geochemistry of Radioactive Isotopes*

*DOI: http://dx.doi.org/10.5772/intechopen.91616*

provided the original work is properly cited.

Department of Geology, College of Science, University of Baghdad, Baghdad, Iraq

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: salihauad2000@yahoo.com

*Geochemistry of Radioactive Isotopes DOI: http://dx.doi.org/10.5772/intechopen.91616*

### **Author details**

initial ratio directly on y-axis. On **Figure 9**, the 87Sr/86Sr increase with decrease 87Rb/86Sr due to decay Rb over time. The slope of ischron is increased accordingly with time. Practically, the *y*-axis is expanded much to displays rocks of geological

*Rb-Sr isochron diagram on axis of equal magnitude showing production of 87Sr as 87Rb is consumed in two*

The original isotopic composition of mantle is basically inherited in the primary basic magma. The alkali ocean-island basalts were investigated for the Rb-Sr system [26]. The results of fourteen wide range type of ocean- island basalt samples plotted on an isochron displayed a proportional correlation to a slop age of about 2B.y representing the time of mantle isolation [25]. This age is known as a mantle isochrones that is also extended to continental igneous rocks [27]. The ratio of 87Sr/86Sr should correct back to initial ratio at the time of magmatism before plotting versus 87Rb/86Sr, so these are termed as pesud-oisochrons. Data of plotting 30 samples from both volcanic and plutonic continental igneous rock suits formed a roughly linear array. The pesud-oisochrons generates from two lines representing crustal contamination of mantle-derived basaltic magma, Scientist replaced that by timing the mantle differentiation events that established mantle domains of different ratio of Rb/Sr in subcontinental lithosphere. This suggestion does not provide reliable results to ascribe age significantly to erupted isochrones. However, the only isotopeisotope mantle isochrones is reliable and can be interpreted and used significantly as

time clearly, and the growth lines become vertical accordingly.

tool for dating the age of mantle differentiation events.

**11.3 Erupted isochro**

*hypothetical samples [25].*

**Figure 9.**

*Geochemistry*

**134**

Salih Muhammad Awadh Department of Geology, College of Science, University of Baghdad, Baghdad, Iraq

\*Address all correspondence to: salihauad2000@yahoo.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### **References**

[1] L'Annunziata MF. Radioactivity Introduction and History. Oxford: Elsevier; 2007. p. 610

[2] L'Annunziata MF. Radioactivity, Introduction and History. The Netherland: Library of Congress Cataloging in Publication Data; 2007. p. 610

[3] Cardarelli F. Encyclopaedia of Scientific Units, Weights and Measures. springer-Germany: Springer-Verlag London Ltd; 2003. ISBN: 978-1-4471-1122-1

[4] Mitchell N, Pérez-Sánchez D, Thorne MC. A review of the behaviour of U-238 series radionuclides in soils and plants. Journal of Radiological Protection. 2013;**33**:R17-R48

[5] Nebel O, Scherer E, Mezger K. Evaluation of the 87Rb decay constant by age comparison against the U–Pb system. Earth and Planetary Science Letters. 2011;**301**:1-8

[6] Jenkin GRT, Ellam RM, Rogers G, Stuart FM. An investigation of closure temperature of the biotite Rb–Sr system: The importance of cation exchange. Geochimica et Cosmochimica Acta. 2001;**65**:1141-1160

[7] White WM. Isotope Geochemistry. New York, USA: Wiley-Blackwell; 2014. p. 496

[8] Gupta MC, McFarlane RD. The natural alpha radioactivity of samarium. Journal of Inorganic and Nuclear Chemistry. 1970;**32**:3425-3432

[9] Lugmair GW, Marti K, Scheinin NB. Incomplete mixing of products from r-, p-, and sprocess nucleosynthesis: Sm-Nd systematics in Allende inclusion EKI-4-1. Lunar Planet. 1978;**IX**:672-674

[10] Beckinsale RD, Gale NH. A reappraisal of the decay constants and branching ratio of 40K. Earth and Planetary Science Letters. 1969;**6**:289-294 [20] Krogh TE. A low contamination

*Geochemistry of Radioactive Isotopes*

decomposition of zircon and extraction of uranium and Pb for isotopic age determination. Geochimica et

*DOI: http://dx.doi.org/10.5772/intechopen.91616*

Cosmochimica Acta. 1973;**37**:484-494

[21] Parrish RR. An improved microcapsule for zircon dissolution in U-Pb geochemistry. Chemical Geology: Isotope Geoscience Section. 1987;**66**:

[22] Croudace IW. A possible error source of silicate wet chemistry caused by insouluble fluoride. Chemical

[23] Patchett PI, Tatsumoto M. A routine high precision method for Lu-Hf isotope

Geology. 1980;**31**:153-155

geochemistry and chronology. Contributions to Mineralogy and Petrology. 1980;**75**:263-267

[24] Nicolyasen IO. Graphic interpretation of discordant age measurements of metamorphic rocks. Annals of the New York Academy of

Sciences. 1961;**91**:189-206

2005. p. 492

**137**

[25] Dickin AP. Radiogenic Isotope Geology. Cambridge University Press;

[26] Sun SS, Hanson GN. Evaluation of the mantle: Geochemical evidence from alkali basalt. Geology. 1975;**3**:297-302

[27] Brooks C, Harts SR, Hofmann A, James DE. Rb-Sr mantle isochrons from oceanic regions. Earth and Planetary Science Letters. 1967;**32**:52-62

method for hydrothermal

99-102

[11] Steiger RJ, Jäger E. Subcommission on geochronology: Convention on the use of decay constants in geo- and cosmocchronology. Earth and Planetary Science Letters. 1977;**36**:359-362

[12] Allegre CJ. Isotope Geology. London: Cambridge University Press; 2008. p. 511

[13] Smoliar MI, Walker RJ, Morgan JW. Re-Os ages of group IIA, IIIA, IVA, and IVB iron meteorites. Science. 1996;**271**: 1099-1102

[14] Begemann F, Ludwig KR, Lugmair GW, Min K, Nyquist LE, Patchett PJ, et al. Call for an improved set of decay constants for geochronological use. Geochimica et Cosmochimica Acta. 2001;**65**:111-121

[15] Shirey SB, Walker RJ. The Re-Os isotope system in cosmochemistry and hightemperature geochemistry. Annual Review of Earth and Planetary Sciences. 1998;**26**:423-500

[16] Jaffey AH, Flynn KF, Glendenin LF. Precision measurement of half-lives and specific activities of 235U and 238U. Physics Review. 1971;**C4**:1889-1906

[17] Rasskazov SV, Brandt SB, Brandt IS. Radiogenic Isotopes in Geologic Processes. Springer Dordrecht Heidelberg London New York, Library of Congress Control Number: 2009938100. New York; 2010

[18] McDougall I, Harrison TM. Geochronology and Thermochronology by the 40Ar/39Ar Method. New York: Oxford University Press; 1999. p. 212

[19] Grove M, Harrison TM. 40Ar diffusion in Fe-rich biotite. American Mineralogist. 1996;**81**:940-951

*Geochemistry of Radioactive Isotopes DOI: http://dx.doi.org/10.5772/intechopen.91616*

[20] Krogh TE. A low contamination method for hydrothermal decomposition of zircon and extraction of uranium and Pb for isotopic age determination. Geochimica et Cosmochimica Acta. 1973;**37**:484-494

**References**

*Geochemistry*

Elsevier; 2007. p. 610

[1] L'Annunziata MF. Radioactivity Introduction and History. Oxford:

branching ratio of 40K. Earth and

Science Letters. 1977;**36**:359-362

[14] Begemann F, Ludwig KR, Lugmair GW, Min K, Nyquist LE, Patchett PJ, et al. Call for an improved

geochronological use. Geochimica et Cosmochimica Acta. 2001;**65**:111-121

[15] Shirey SB, Walker RJ. The Re-Os isotope system in cosmochemistry and hightemperature geochemistry. Annual Review of Earth and Planetary Sciences.

[16] Jaffey AH, Flynn KF, Glendenin LF. Precision measurement of half-lives and specific activities of 235U and 238U. Physics Review. 1971;**C4**:1889-1906

[17] Rasskazov SV, Brandt SB, Brandt IS.

Heidelberg London New York, Library

Geochronology and Thermochronology by the 40Ar/39Ar Method. New York: Oxford University Press; 1999. p. 212

Radiogenic Isotopes in Geologic Processes. Springer Dordrecht

of Congress Control Number: 2009938100. New York; 2010

[18] McDougall I, Harrison TM.

[19] Grove M, Harrison TM. 40Ar diffusion in Fe-rich biotite. American

Mineralogist. 1996;**81**:940-951

set of decay constants for

1998;**26**:423-500

1099-1102

Planetary Science Letters. 1969;**6**:289-294

[11] Steiger RJ, Jäger E. Subcommission on geochronology: Convention on the use of decay constants in geo- and cosmocchronology. Earth and Planetary

[12] Allegre CJ. Isotope Geology. London: Cambridge University Press; 2008. p. 511

[13] Smoliar MI, Walker RJ, Morgan JW. Re-Os ages of group IIA, IIIA, IVA, and IVB iron meteorites. Science. 1996;**271**:

[2] L'Annunziata MF. Radioactivity, Introduction and History. The Netherland:

Library of Congress Cataloging in Publication Data; 2007. p. 610

[3] Cardarelli F. Encyclopaedia of Scientific Units, Weights and Measures. springer-Germany: Springer-Verlag

[4] Mitchell N, Pérez-Sánchez D, Thorne MC. A review of the behaviour of U-238 series radionuclides in soils and

plants. Journal of Radiological Protection. 2013;**33**:R17-R48

[5] Nebel O, Scherer E, Mezger K. Evaluation of the 87Rb decay constant by

age comparison against the U–Pb system. Earth and Planetary Science

[6] Jenkin GRT, Ellam RM, Rogers G, Stuart FM. An investigation of closure temperature of the biotite Rb–Sr system: The importance of cation exchange. Geochimica et Cosmochimica Acta.

[7] White WM. Isotope Geochemistry. New York, USA: Wiley-Blackwell; 2014.

[8] Gupta MC, McFarlane RD. The natural alpha radioactivity of samarium. Journal of Inorganic and Nuclear Chemistry. 1970;**32**:3425-3432

[9] Lugmair GW, Marti K, Scheinin NB. Incomplete mixing of products from r-, p-, and sprocess nucleosynthesis: Sm-Nd systematics in Allende inclusion EKI-4-1. Lunar Planet. 1978;**IX**:672-674

[10] Beckinsale RD, Gale NH. A reappraisal of the decay constants and

Letters. 2011;**301**:1-8

2001;**65**:1141-1160

p. 496

**136**

London Ltd; 2003. ISBN: 978-1-4471-1122-1

[21] Parrish RR. An improved microcapsule for zircon dissolution in U-Pb geochemistry. Chemical Geology: Isotope Geoscience Section. 1987;**66**: 99-102

[22] Croudace IW. A possible error source of silicate wet chemistry caused by insouluble fluoride. Chemical Geology. 1980;**31**:153-155

[23] Patchett PI, Tatsumoto M. A routine high precision method for Lu-Hf isotope geochemistry and chronology. Contributions to Mineralogy and Petrology. 1980;**75**:263-267

[24] Nicolyasen IO. Graphic interpretation of discordant age measurements of metamorphic rocks. Annals of the New York Academy of Sciences. 1961;**91**:189-206

[25] Dickin AP. Radiogenic Isotope Geology. Cambridge University Press; 2005. p. 492

[26] Sun SS, Hanson GN. Evaluation of the mantle: Geochemical evidence from alkali basalt. Geology. 1975;**3**:297-302

[27] Brooks C, Harts SR, Hofmann A, James DE. Rb-Sr mantle isochrons from oceanic regions. Earth and Planetary Science Letters. 1967;**32**:52-62

**Chapter 8**

**Abstract**

**1. Introduction**

**139**

Exploration for Fe-Mn Oxides

Soil: A Case Study of Part of

Northwestern Nigeria

with Zr+Th+Pd+Mo+V+Sn+Cr+Ce+InSc+P+Pb association.

*Olufemi Sijuade Bamigboye*

Using Geochemical Signatures in

Part of northwestern Nigeria was investigated with the aim of delineating concealed mineralization using geochemical signatures in soils. To achieve this, 30 selected soil samples were analysed geochemically. The result of the elemental analysis was subjected to Principal Component Analysis (PCA) and isograde plotting, while selected elements were correlated. From the geochemical result, most of the analysed elements have anomalous value in the southern part of the area, while the least values are in the southwestern. From the PCA analysis, six factor groups were distinct. The factor groups were interpreted geochemical to fingerprint mineralization in the area. The result of correlation analysis shows that Fe is negatively correlated with most of the correlated elements. The study concluded that the central part of the study area is mineralized with both manganite and goethite. In addition, manganese mineralization is indicated by elemental association: Zn+As+ Be+Bi+Co+Nb+Ni+CsP+Al+Ca+Cd+Li+K, while iron mineralization is indicated

**Keywords:** manganite, goethite, Kaoje, exploration geochemistry, soil survey

Traditional exploration geochemistry usually employs earth materials such as rock, stream sediment and soil to detect unusual concentration of elements that may serve as pathfinder for concealed ore body [1–3]. The distribution of pathfinder elements in these media especially stream sediment and soil is governed by weathering and hydromorphic conditions of the area under investigation in addition to the mobility of such elements. Despite their dispersion, trace and rare earth elements still retain their bedrock characteristics. These elements are adsorbed unto surfaces of weathered products and possess the ability to remain on the surfaces of these weathered particles for long periods unless they are mobilized by decomposition processes such as redox conditions [4]. Bowen [5] believes that the residence time of these elements in temperate soils is not the same. For example, the residence time of Pb is between 740 and 5900 years, Zn has a residence time of 70–510 years, 13–1100 years is the residence time for Cd, and 310–1500 years is the residence time for Cu, while the residence time in tropical soils is 40 years due to the shorter rate of

#### **Chapter 8**
