Page 260 - Essentials of physical chemistry

222 Essentials of Physical Chemistry

The circuit also includes a battery for a voltage source and a variable resistor to adjust the voltage of
the battery output, but note especially that the polarity of the battery is opposite to the polarity of the
phototube! This arrangement is called a ‘‘bucking potential’’ and it opposes the current flow from
the phototube due to a voltage controlled by the variable resistor (the small slash of the battery
symbol is the negative plate, the larger slash is the positive plate). Assuming a white light source, a
slit and a prism can be used to select the color of the light. It was found the photocurrent ceased as
the color reached a limit in the red direction. The experiment was designed to use the adjustable
bucking potential to find the voltage on the voltmeter at the bottom of the circuit that would stop
the current flow reading on the ammeter. A series of stopping voltages could be measured and
related to the wavelength or frequency of the light but that is not the main effect. In 1905,
Einstein [3] published a very important paper explaining the main meaning of the experimental
data by pointing attention to the red-most cutoff frequency after which the experiment no
longer worked.
Einstein postulated that energy from the light was being used to knock electrons out of the
surface of the metal and that energy was converted into kinetic energy of the ejected electron. Note
this experiment depended on the ability to generate a vacuum inside the tube or else the electron
would simple collide with a gas molecule and probably form an anion. Einstein’s brilliant conclu-
sion was that the frequency of the red-most color where the photocurrent became zero no matter
what the bucking potential was represented the energy required to remove the electron from the
metal and he called it the Work Function (W f ) (Figure 10.8). Although it is not used in the basic
equation to follow, it is important to know that Einstein postulated that the energy chunks of the
light were discrete particles called ‘‘photons.’’ This started a long discussion in Science over what is
called the ‘‘wave-particle duality’’ as to how Maxwell’s classical electromagnetic waves could be
quantized. The best answer is that there are ‘‘wave packet pulses’’ centered at a given frequency by
very slight differences in the main frequency but more mathematics (Fourier analysis) would be
needed to show this. First we can plot the ‘‘stopping potential’’ of the bucking voltage that stops the
photoelectron flow at a series of wavelengths converted to frequencies as shown in Figure 10.9 for
sodium metal. It is clear from the graph that there will be zero photocurrent at n 0 which is at 2.3591
14
14
eV and the slope is 0.4134 eV=10 Hz, but the line stops to the left of 2.3591 eV at 5.7043 10 Hz
or l ¼ 5256 Å. Plotted against frequency this is means we can equate the kinetic energy of the flying
electron to (Table 10.1)
mV 2
¼ C(n n 0 ):
2

One might ask what is the constant C? Einstein then used Planck’s proportionality constant and
equated the total energy of the incoming light photon to the kinetic energy and the energy to knock
the electron out of the metal, the ‘‘work function’’ W f .

mV 2 mV 2
or ¼ hn W f ¼ h(n n 0 ) ¼ C(n n 0 ) and so C ¼ h!
2 2
E ¼ hn ¼ W f þ
Given the data is only reliable to the nearest millivolt (0.001 eV), we can convert the slope to joules
14 19 34
as h ffi (0.4134 eV=10 Hz) (1.60217653 10 J=eV) ¼ 6.6234 10 J s That is very
interesting but maybe we ought to also plot the limiting stopping potentials versus the n 0 frequencies
for a number of metals to see if that has a linear dependence. We use the W f values from the CRC
Handbook [8], which only gives three significant figures for the values in eV so we have used the
most precise formulas to convert to n 0 in attempt to get a more precise value for h. It is again clear
that the linear fit is very good but the slope is slightly different at 0.4136 (eV=10 14 Hz) that leads to
h ¼ 6.626602128 10 34 J s, which should be rounded to h ¼ 6.627 10 34 J s. A thinking