Physical Chemistry Third Edition

23.1 Emission/Absorption Spectroscopy and Energy Levels 951

levels correspond to photon energies in the infrared region, and spacings between

rotational energy levels correspond to photon energies in the microwave region. Spac-

ings between translational energy levels are too small to observe spectroscopically.

Photochemistryinvolves absorption of photons that can break chemical bonds or

cause transitions to reactive excited states. Typical chemical bond energies are roughly

400 to 1000 kJ mol−^1. Photons with energies large enough to break chemical bonds lie

in the ultraviolet region.

EXAMPLE23.1

Find the frequency and wavelength of a photon with enough energy to break a chemical bond

with bond energy of 4.31 eV (corresponding to 416 kJ mol−^1 ), which is the average bond

energy of a C–H bond.

Solution

ν

E

h



(4.31 eV)(1. 602 × 10 −^19 J (eV)−^1 )

6. 6261 × 10 −^34 Js

 1. 04 × 1015 s−^1

λ

2. 9979 × 108 ms−^1

1. 04 × 1015 s−^1

 2. 88 × 10 −^7 m288 nm

Exercise 23.1

Aneinsteinis a mole of photons. Find the energy per photon and per einstein for

a.Microwave radiation withλ 1 .00 cm

b.Infrared radiation withλ 3. 00 μm

c.Ultraviolet radiation withλ 200 .0nm

d.X-radiation withλ 100 .0pm

The Quantum Mechanics of Spectroscopic Transitions

Our discussion of quantum mechanics in previous chapters has focused on station-

ary states of atomic and molecular systems as described by the time-independent

Schrödinger equation. Spectroscopy involves a time-dependent process, the evolution

of the state of a system containing atoms or molecules plus electromagnetic radiation.

Electromagnetic radiation consists of an oscillating electric field and an oscillating

magnetic field as depicted in Figure 14.9. Because an electric field puts a force on

any charged particle and a magnetic field puts a force on a moving charged particle,

both of these fields interact with the nuclei and electrons of an atom or molecule, and

both can cause absorption or emission of energy. A transition produced by the elec-

tric field is called anelectric dipole transition, and a transition due to the magnetic

field is called amagnetic dipole transition. The electric dipole transitions dominate in

optical spectroscopy. Magnetic dipole transitions are involved in nuclear magnetic res-

onance (NMR) spectroscopy and electron spin resonance (ESR) spectroscopy, which

we discuss in the next chapter.

Time-dependent perturbation theory is applied to study electric dipole transi-

tions. We give a brief introduction and quote some of the results. The Hamiltonian