**8. The photoelectric effect without photons** [Ragazas 2010k]

Photoelectric emission has typically been characterized by the following experimental facts *(some of which can be disputed, as noted)*:


*Explanation of the Photoelectric Effect without the Photon Hypothesis:* Let be the rate of radiation of an incident light on a metal surface and let be the rate of absorption of this radiation by the metal surface. The combined rate locally at the surface will then be . The radiation energy at a point on the surface can be represented by <sup>0</sup> ( ) *<sup>t</sup> Et Ee* , where *E*0 is the intensity of radiation of the incident light. If we let be the *accumulation of energy* locally at the surface over a time pulse , then by *Characterization 1* we'll have that *E* . If we let Planck's constant *h* be the *accumulation of energy* for an electron, the

number of electrons *ne* over the pulse of time will then be *ne <sup>h</sup>* and the energy of an electron *Ee* will be given by

$$
\Delta E\_e = \frac{\Delta E}{n\_e} = h(\nu - a) \tag{10}
$$

Since 0 0 <sup>0</sup> *<sup>u</sup> <sup>e</sup>* <sup>1</sup> *E e du E* , we get the *photoelectric current <sup>I</sup>* ,

The Thermodynamics *in* Planck's Law 707

The graphs in Fig. 5 match the above experimental data to various graphs (in red) of

*A=0.13 b=1.98 c=5.95 d=0,07 A=0.09 b=2.07 c=4.88 d=0.09 A=0.05 b=1.41 c=3.04 d=0.18* 

The above graphs (Fig. 5) seem to suggest that Eq. (11) agrees well with the experimental data showing the asymptotic behavior of the (photocurrent) v (energy) curves. But more

> 0

= %-change of

0

*h* (Planck's constant being the minimal

0

 

*x*

*t t E h h*

 

= "distance per cycle of change" and

*x*

and

0 *t* 

 .

that can be

= 'cycle of change'. For

**9. Meaning and derivation of the De Broglie equations** [Ragazas 2011a]

= "cycle of change per time". We can rewrite these as <sup>0</sup>

<sup>0</sup> *h h*

 

*x x*

*p*

and

(a) (b) (c)

systematic experimental work is needed.

 

corresponding *x* and *t* we can write,

measured) we get the *de Broglie equations:*

( , ) ( ,) *x t xt* . We can write

Fig. 4.

Fig. 5.

Consider 0 00 

> 0 *t*

Taking limits and letting 0

equation (12)

$$I = \frac{n\_c}{\tau} = \frac{\eta}{h\tau} = E\_0 \left| \frac{e^{(\nu - \alpha)\tau} - 1}{h(\nu - \alpha)\tau} \right| \tag{11}$$

The absorption rate is a characteristic of the metal surface, while the pulse of time is assumed to be constant for fixed experimental conditions. The quantity *e* 1 *h* in

equation (10) would then be *constant*.

Combining the above and using (10) and (11) we have *The Photoelectric Effect:* 


*kT Note:* Many experiments since the classic 1916 experiments of Millikan have shown that there is photoelectric current even for frequencies below the threshold, contrary to the explanation by Einstein. In fact, the original experimental data of Millikan show an asymptotic behavior of the (photocurrent) vs (voltage) curves along the energy axis with no clear 'threshold frequency'. The photoelectric equations (10) and (11) we derived above

agree with these experimental anomalies, however. In an article Richard Keesing of York University, UK , states,

*I noticed that a reverse photo-current existed … and try as I might I could not get rid of it.* 

*My first disquieting observation with the new tube was that the I/V curves had high energy tails on them and always approached the voltage axis asymptotically. I had been brought up to believe that the current would show a well defined cut off, however my curves just refused to do so.* 

*Several years later I was demonstrating in our first year lab here and found that the apparatus we had for measuring Planck's constant had similar problems.* 

*After considerable soul searching it suddenly occurred on me that there was something wrong with the theory of the photoelectric effect … [Keesing 2001]* 

In the same article, taking the original experimental data from the 1916 experiments by Millikan, Prof. Keesing plots the graphs in Fig. 4.

In what follows, we analyze the asymptotic behavior of equation (11) by using a function of the same form as (11).

$$f(\mathbf{x}) = \frac{A\left(e^{b(\mathbf{x}-c)} - \mathbf{1}\right)}{\mathbf{x} - c} + d \tag{12}$$

*Note: We use d since some graphs typically are shifted up a little for clarity.* 

Fig. 4.

706 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

<sup>1</sup> *ne <sup>e</sup> I E h h*

would be negative and so there will be no photoelectric current. (by (10) above) *(see* 

by *Conclusion* 7 **Section 3**.

3. If *Ee* is taken to be the kinetic energy of a photoelectron, then for incident light with

4. The photoelectric current is almost instantaneous ( <sup>9</sup> 10 sec. ), since for a single

*Note:* Many experiments since the classic 1916 experiments of Millikan have shown that there is photoelectric current even for frequencies below the threshold, contrary to the explanation by Einstein. In fact, the original experimental data of Millikan show an asymptotic behavior of the (photocurrent) vs (voltage) curves along the energy axis with no clear 'threshold frequency'. The photoelectric equations (10) and (11) we derived above

*I noticed that a reverse photo-current existed … and try as I might I could not get rid of it. My first disquieting observation with the new tube was that the I/V curves had high energy tails on them and always approached the voltage axis asymptotically. I had been brought up to believe that the current would show a well defined cut off, however my curves just refused to do so. Several years later I was demonstrating in our first year lab here and found that the apparatus* 

*After considerable soul searching it suddenly occurred on me that there was something wrong* 

In the same article, taking the original experimental data from the 1916 experiments by

In what follows, we analyze the asymptotic behavior of equation (11) by using a function of

*bx c A e f x d x c*

<sup>1</sup>

(12)

current *I* is proportional to the intensity *E*0 of the incident light. (by (11) above)

assumed to be constant for fixed experimental conditions. The quantity

Combining the above and using (10) and (11) we have *The Photoelectric Effect:* 

2. The energy *Ee* of a photoelectron depends only on the frequency

less than the 'threshold frequency'

*kT*

intensity *E*0 of the incident light. It is given by the equation *E h <sup>e</sup>*

 <sup>0</sup>

(11)

 *e* 1

and not on the

where *h* is

 

*h* 

 

the kinetic energy of a photoelectron

and fixed metal surface, the photoelectric

is a property of the metal surface. (by (10)

is

in

 

> 

is a characteristic of the metal surface, while the pulse of time

The absorption rate

above)

frequency

*Note below)* 

the same form as (11).

1. For incident light of fixed frequency

Planck's constant and the absorption rate

photoelectron we have that <sup>9</sup> 10 sec. *<sup>h</sup> <sup>t</sup>*

agree with these experimental anomalies, however.

Millikan, Prof. Keesing plots the graphs in Fig. 4.

In an article Richard Keesing of York University, UK , states,

*we had for measuring Planck's constant had similar problems.* 

( )

*Note: We use d since some graphs typically are shifted up a little for clarity.* 

*with the theory of the photoelectric effect … [Keesing 2001]* 

equation (10) would then be *constant*.

The graphs in Fig. 5 match the above experimental data to various graphs (in red) of equation (12)

Fig. 5.

The above graphs (Fig. 5) seem to suggest that Eq. (11) agrees well with the experimental data showing the asymptotic behavior of the (photocurrent) v (energy) curves. But more systematic experimental work is needed.
