Page 100 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch08 Elementary Physical Chemistry

Introduction to Quantum Theory 85

the Laws of Maxwell, in other words, would be wave-like. But Einstein
argued that these ideas are inconsistent. He maintained that if energy is
absorbed from the heat source in quanta, it must also emit radiation energy
in the form of quanta, clearly implying that radiation is particle-like.
Einstein then introduced the notion that light consists of indivisible
units (later called photons), the energy of which is ε = hν,where h is
Planck’s constant and ν the frequency. Planck’s constant has the value
2 −1
h =6.626 × 10 34 Js or h =6.626 kg m s .

Comment: It is ironical that Einstein who brought down Newton’s
classical mechanics with relativity resurrected Newton’s corpuscular
theory of light.

Einstein’s idea was not based strictly on logic, as compelling as that
was; but by postulating the existence of indivisible light units, he was able
to explain the photo-electric effect.
According to Einstein, electrons in a metal are knocked out by photons.
The energy of a photon must be equal to or exceed the attractive energy
between the electron and the positive charge of the metal. This energy is
called the work-function and is denoted as φ. If there is excess energy, it
is carried off by the emitted electron in the form of kinetic energy. Thus,
KE elecr = ε phot − φ.

8.2.3. Heat Capacity of Solids

Solids consist of atoms which are oscillating. According to classical theory,
the average energy of an oscillator in 3-D is 3kT ,where k is the Boltzmann
constant equal to R/N A ,(N A being Avogadro’s number). The vibrational
molar energy is 3RT and the heat capacity is C V =3R (the value of Dulong
and Petit). The actual heat capacity, as shown in Fig. 8.1, is constant with a
value of 3R; but as the temperature is lowered, the heat capacity decreases,
and at0 Kitis zero.
To explain this, Einstein invoked Planck’s hypothesis that the energy
of an oscillator has to be quantized. This produced a heat capacity curve
which is very similar to the observed one. The formula was further improved
by Debye who did essentially what Einstein did but considered the solid
to vibrate with a range of frequencies rather than a single frequency as
Einstein had done.