Concise Physical Chemistry

c15 JWBS043-Rogers September 13, 2010 11:28 Printer Name: Yet to Come

236 EARLY QUANTUM THEORY: A SUMMARY

Wavelength

Lyman Balmer Paschen

FIGURE 15.1 The hydrogen atom emission spectrum (not to scale). The wavelengthsλof

the lines correspond to differences in energy between allowed levels in the hydrogen atom

according to the equationE=hν=hc/λ,wherecis the speed of light,his Planck’s constant,

andνis the frequency (Planck, 1901).

hydrogen atom—shows regular groupings that invite closer attention and theoretical

explanation. Three of these groupings are shown in Fig. 15.1.

The experimental facts had been known for a half century before Schrodinger’s ̈

time and had been partly explained in 1913 by Niels Bohr, who imposed a quantum

number on the angular momentum of the orbital electron in hydrogen to arrive at a set

of energy levels corresponding to stationary states of the atom. Transitions from one

energy level to another correspond quite precisely to lines in the hydrogen spectrum,

but it was not clear where the quantum number came from and it was not possible to

generalize the Bohr system to more complicated atoms and molecules (Fig. 15.2).

15.2 EARLY QUANTUM THEORY

Early quantum theory showed that not only the hydrogen spectrum, but also several

other important problems, can be solved by taking into account a frequencyνasso-

ciated with the energy of particles according to the Planck equationE=hν.Butthe

method, no matter how well it worked, still lacked a theoretical base and a logically

consistent means of application, modification, and improvement. De Broglie (1924,

1926) pointed out that energyEof a moving particle implies momentump. Frequency

νimplies a wavelength. Therefore, if the Planck equation works (which it does),

E x 10

-19

, J

-25

-20

-15

-10

-5

0

FIGURE 15.2 The first six solutions of the H atom energy calculated by Bohr (1913). The

energies are negative because the electron is bound to the proton.