Chemistry 475 (Amar) - Spring, 2009 

The Photoelectric Effect
(©2009, François G. Amar, All rights reserved)

In 1902, P. Lenard and others systematically studied the photoelectric effect in order to investigate the circumstances under which metal surfaces will emit electron (-rays) when they are exposed to light.

 

Consider the case of sodium metal.

Observation #1: light of wavelength =520 nm (green light) does not lead to emission of any electrons. Increasing the intensity of the light does not help!

Observation #2: light of wavelength =450 nm (blue light) does lead to emission of "photoelectrons".

Observation #3: light of wavelength =400 nm (violet light) leads to emission of "photoelectrons" with a higher kinetic energy than those which come off under irradiation at 450 nm.

Observation #4: increasing the intensity of light of wavelength =400 nm (violet light) leads to emission of more "photoelectrons" (higher current) but with the same kinetic energy as for the lower intensity irradiation.

Here is some data for sodium:

(nm)
electron KE (J)
750
0
700
0
650
0
600
0
500
0
475
0
400
5.48x10-20
350
1.27x10-19
300
2.18x10-19
250
3.49x10-19
200
5.45x10-19

Let us convert the wavelength to frequency using =c/

(s-1)
electron KE (J)
3.99x1014
0
4.28x1014
0
4.61x1014
0
4.99x1014
0
5.99x1014
0
6.30x1014
0
7.49x1014
5.48x10-20
8.56x1014
1.27x10-19
9.99x1014
2.18x10-19
1.20x1015
3.49x10-19
1.50x1015
5.45x10-19

If we now look for a best-fit straight line through the data ( y= mx+b), we get the following:

The straight line equation we get has the form

y= mx+b

where here

y is KE

x is

m=6.59x10-34 J-s

(note this is Planck's constant, h)

b=-4.39x10-19J (we'll let W=-b)

So we get Einstein's equation for the photoelectric effect:

KE = h-W

W (the metal's work function) is the minimum energy photon required to eject an electron

An alternative way to write this equation is

h= W + KE

which expresses the fact that the energy of the photon is partitioned between the minimum needed to eject the electron and the remainder goes into kinetic energy.

 

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