Eparticle¼hv
v¼frequency of the light(4.4)
These particles became known as photons (the word was coined by Gilbert Lewis,
ca. 1923, but his photon was not the particle of modern physics). If the energy of the
photon before it removes an electron from the metal is equal to the energy required to
tear the electron free of the metal, plus the kinetic energy of the free electron, then
hv¼Wþ^1 = 2 mev^2 (4.5)W¼work function of the metal, energy needed to remove an electron (with no
energy left over),me¼mass of an electron,v¼velocity of electron ejected by the
photon,^1 = 2 mev^2 ¼kinetic energy of the free electron
Rearranging Eq.4.5:
(^1) = 2 mev^2 ¼hv"W (4.6)
Thus a plot of the kinetic energies of the electronsðÞ^1 = 2 mev^2 versus the frequency
nof the light should be a straight line of positive slope (h; this is one way to
find Planck’s constant) intersecting thenaxis at a positive value (n¼W/h), as
experiment indeed showed (Fig.4.3).
Planck’s explanation of the blackbody radiation curves (1900 [ 4 ]) and Einstein’s
explanation of the facts of the photoelectric effect (1905 [ 7 ]) indicated that the
flow of energy in physical processes did not take place continuously, as had
been believed, but rather jerkily, in discrete jumps, quantum by quantum. The
contributions of Planck and Einstein were the signal developments marking the
birth of quantum theory and the transition from classical to modern physics.
4.2.2 Radioactivity
Brief mention of radioactivity is in order because it, along with quantum mechanics
and relativity, transformed classical into modern physics. Radioactivity was
discovered by Becquerel in 1896. However, an understanding of how materials
like uranium and radium could emit, over the years, a million times more energy
than would be permitted by chemical reactions, had to await Einstein’s special
theory of relativity (Section 4.2.3), which showed that a tiny, unnoticeable decrease
in mass represented the release of a large amount of energy.
4.2.3 Relativity
Relativity is relevant to computational chemistry because it must often be explicitly
taken into account in accurate calculations involving atoms heavier than about
4.2 The Development of Quantum Mechanics. The Schr€odinger Equation 91