Page 437 - Schaum's Outline of Theory and Problems of Applied Physics

422 ATOMIC PHYSICS [CHAP. 34

SOLVED PROBLEM 34.7
To what temperature must a hydrogen sample be heated so that the average molecular energy equals the
binding energy of the hydrogen atom?
The binding (or ionization) energy of the hydrogen atom is 13.6 eV = 2.18 × 10 −18 J. Since the average
3
molecular energy is a gas whose absolute temperature T is equal to kT , here
2
3
kT = E
2
2E (2)(2.18 × 10 −18 J) 5
T = = = 1.05 × 10 K
3k (3)(1.38 × 10 −23 J/K)

ATOMIC SPECTRA

When a gas or vapor is excited by the passage of an electric current, light is given off which consists of certain
specific wavelengths. Every element has such a characteristic emission line spectrum. The wavelengths in this
spectrum fall into definite series whose member wavelengths are related by simple formulas.
When white light is passed through a cool gas or vapor, light of certain specific wavelengths is absorbed.
The wavelengths in the resulting absorption line spectrum correspond to a number of the wavelengths in the
emission spectrum of that element.
Line spectra owe their origin to the presence of energy levels in atoms. An atom in an excited state can
remain there only a brief time (normally about 10 −8 s) before dropping to a lower state. The difference in energy
appears as a photon of frequency f , where
E initial − E final = hf

Figure 34-1 is an energy-level diagram which shows the possible transitions in the hydrogen atom that are
responsible for its emission line spectrum. The larger the energy difference between initial and final energy states,
as indicated by the lengths of the arrows, the higher the frequency of the photon that is emitted. The names of
the various spectral series in hydrogen are indicated.
An absorption spectrum is produced by transitions in the opposite direction, from the ground state to excited
states. Consider atoms illuminated by a beam of light whose spectrum is continuous (that is, a spectrum which

Fig. 34-1