Page 104 - Bruno Linder Elementary Physical Chemistry

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

Introduction to Quantum Theory 89

With these assumptions, Bohr was able to generate the well-known
empirical formulas for the emission of radiation by excited hydrogen atoms.
They are
2
2
ν/c = R H (1/1 − 1/n ) n =2, 3,... Lyman Series (8.2a)
2
2
ν/c = R H (1/2 − 1/n ) n =3, 4,... Balmer Series (8.2b)
2
2
ν/c = R H (1/3 − 1/n ) n =4, 5,... Paschen Series (8.2c)
Note: Bohr’s theory was essentially classical in nature except for the
assumption of quantization of energy (really of angular momentum of
the moving electron) and the photon nature of radiation. This forced
him to postulate the conditions 4 and 5.

Bohr’s prediction of radiation of the hydrogen atom was in almost
perfect agreement with experiments, suggesting that the theory of he atom
was solved. But when the theory was applied to He, the results were not
good, and when applied to heavier atoms, the theory failed miserably.
The phenomenal success of the Bohr theory of the hydrogen atom,
followed by swift decline, was so disturbing that many scientists were
beginning to have serious doubts about the generality of science.

8.5. Louis de Broglie
Then, in 1923, Louis de Broglie, a physics student at the Sorbonne, sub-
mitted a dissertation in which he made a startling discovery. Rummaging
through Einstein’s theory of relativity, he concluded that matter must
consist of waves — matter waves.
His reasoning (highly simplified here) may have been based on the
following kinds of analogies: For photons, ε = hν. Photons have zero rest
mass, but not when in motion. Using Einstein’s relativity formula E = mc 2
2
and his expression for the photon energy ε = hν = mc produced
hν/c = mc = p, (8.3a)

p being the momentum. Thus, for photons

h/mc = h/p = c/ν = λ (8.3b)