Page 251 - Essentials of physical chemistry

10 Early Experiments

in Quantum Physics

INTRODUCTION
We tried to introduce the idea of quantization in Chapter 9 as a completion of a one semester course.
However, we skipped over some really interesting events in the history of Science between 1900
and 1913 when Bohr derived the quantized energy of the H atom. First we want to carry out the
1901 Planck derivation of the formula for blackbody radiation [1]. Many texts just show the curve,
write e ¼ hn, and move on. As a student, this author found that limited explanation very frustrating
since energy quantization is a fundamental concept. Even among graduate texts in quantum
mechanics, we are aware of only one that does the complete treatment which we will draw upon
for the mathematics [2] but supplement with a narrative that we have found helpful to students over
the years. Then in 1905, Albert Einstein (1879–1955), one of the most influential scientists of all
time, gave an explanation of the photoelectric effect [3] for which he received the Nobel Prize in
1921. Even reducing our list to essential topics, we need to discuss the Davisson–Germer
experiment [4]. The photoelectric effect introduces the idea that light waves can act as particles
while the Davisson–Germer experiment showed that particles can act like waves and confirmed the
De Broglie equation [5]. However, you can be assured that it will not be as difficult as you might
have anticipated and if you can absorb the meaning of just these three key experiments you should
be able to begin thinking in terms of quantum mechanics! Despite our slow historical development,
this is 2010 and we have to get to the twenty-first century somehow!

STEFAN–BOLTZMANN LAW: RELATING HEAT AND LIGHT—PART I
We do not want you to forget the thermodynamics you learned in earlier chapters but historically
there was a shift in science with the idea of energy quantization in 1900. There was awareness of the
connection between heat and light before the late 1800s but one of the first quantitative treatments
was by Boltzmann and his doctoral mentor Jozef Stefan (1835–1893), an Austrian physicist and
Ludwig Boltzmann’s PhD thesis advisor. Prior to the concept of quantization, the arguments were
thermodynamic in nature. Recall the HUGA equations of thermodynamics and the form of the first
law for a closed system as dU ¼ TdS PdV and the equation for the Helmholtz free energy
2 2
q A q A qS qP
dA ¼ Sdt PdV. Equating the second derivatives ¼ ) ¼
qTqV qVqT qV qT
T V

qU qP
which will be useful here and leads to ¼ T P. Another fact needed is beyond the
qV qT
T V
level of this text as a relationship that comes from Maxwell’s electromagnetic theory in that there is
r
a weak ‘‘electromagnetic pressure’’ P ¼ , often discussed in Astronomy relative to intense light
3
from stars. This feeble pressure is predicted by Maxwell’s equations for electromagnetic waves but
its measurement is made difficult by thermal gas heating even in a partial vacuum. The common
Crookes radiometer (http:==www.strangeapparatus.com=Crooke_s_Radiometer.html) actually works
via thermal heating of air around small paddle wheel vanes exposed to intense light in a partial
vacuum. However, in 1933, Bell and Green [6] improved on earlier experiments and succeeded in
measuring this small pressure to rotate some small vanes (glass plates) suspended by delicate quartz
213