Physical Chemistry Third Edition

960 23 Optical Spectroscopy and Photochemistry

For then2ton1 transition

1

λ

(109678 cm−^1 )

(

1

1

−

1

4

)

82258 cm−^1

λ

1

82258 cm−^1

 1. 2157 × 10 −^5 cm 121 .568 nm, in the ultraviolet

Exercise 23.3

From Rydberg’s formula in Eq. (14.4-10), find the wavelength and frequency of the photons

emitted by a hydrogen atom undergoing then 3 →n2 transition and then 4 →n 3

transition. In what spectral range (visible, ultraviolet, or infrared) does each lie?

Multielectron Atoms

If orbital wave functions are used to calculate transition dipole moments, the following

selection rules are obtained for multielectron atoms:^6

Selection Rules for Multielectron Atoms

∆L± 1 (23.2-2a)

∆S 0 (23.2-2b)

∆J0,±1(0→0 not allowed) (23.2-2c)

∆MJ0,±1(0→0 not allowed for∆J0) (23.2-2d)

whereJis the quantum number for the total electronic angular momentum andMJis

the quantum number for itszcomponent. Because approximate wave functions were

used to derive these selection rules, forbidden transitions do occur. The most important

selection rule is that∆S0. For example, transitions between singlet and triplet states

are forbidden.

PROBLEMS

Section 23.2: The Spectra of Atoms

23.9A positronium atom^7 consists of a positron, which is an

antiparticle with the same mass as an electron and the

same charge as a proton, and one electron. Find the

wavelengths of the photons emitted in the following

“electronic” transitions:

a.n3ton 2

b.n4ton 2

c.n5ton 2

d.n6ton 2

Compare these wavelengths with those of a normal

hydrogen atom.

23.10A tritium atom has a nucleus that contains a proton and

two neutrons. Its atomic mass is approximately 3.0 amu.

Find the wavelengths of the photons emitted in the

following electronic transitions:

(^6) J. C. Davis,op. cit., pp. 256–257 (note 2).
(^7) The dipositronium molecule has been synthesized. It persisted for less than a nanosecond before the positrons and electrons annihilated each other.See
D. B. Cassidy and A. P. Mills, Jr.,Nature, 449, 195 (2007).