Physical Chemistry Third Edition

992 23 Optical Spectroscopy and Photochemistry

whereMrepresents a molecule of the sample substance. The kinetic energy of the

ejected electron is measured, and the difference in energy between a photon of the inci-

dent radiation and the kinetic energy of the electron is taken to be the ionization energy

of the ejected electron. Usually several different ionization energies are obtained. If

the electronic wave function is approximated as an orbital wave function the ejected

electron will come from a specific orbital. According toKoopman’s theoremthe ion-

ization energy is equal to the magnitude of the orbital energy of the orbital from which

the electron came.^27

Figure 23.20 shows the photoelectron spectrum of N 2 , using 58.4 nm ultraviolet

radiation. The kinetic energy of the electrons increases from left to right so that the

ionization energy increases from right to left. There are three sets of lines, each corre-

sponding to ionization from a different orbital. The ground-level electron configuration

of N 2 is

(σg 1 s)^2 (σ∗u 1 s)^2 (σg 2 s)^2 (σ∗u 2 s)^2 (πu 2 p)^4 (σg 2 p)^2

The rightmost set of lines arises from removal of an electron from theσg 2 pbonding

orbital. The center set of lines arises from removal of an electron from aπu 2 pbonding

orbital, and the leftmost set of lines arises from removal of an electron from theσ∗u 2 s

antibonding orbital.

The lines within each set correspond to different vibrational states of the ion pro-

duced by the ionization. The absorption of a photon with removal of an electron is

sufficiently rapid that the nuclei do not have time to move appreciably, as in the Franck–

Condon principle. The ionization potential that is determined through photoelectron

spectroscopy is referred to as the “vertical” ionization energy, as represented by a ver-

tical line in a diagram such as that of Figure 23.11. In the nitrogen spectrum it appears

that the ionization to thev1 vibrational state of the ion is the most probable pro-

cess for the center set of lines, while in the other two sets the transition to thev 0

vibrational state is the most probable transition.

0.2

21.0 20.0 19.0 18.0

lonization energy/eV

Photoelectron energy/eV

Counts/s

17.0 16.0 15.0

6.2

2390 cm^21

1810 cm^21

2150 cm^21

18.76 eV

16.69 eV

15.58 eV

Figure 23.20 Photoelectron Spectrum of Nitrogen.From I. N. Levine,Molecular

Spectroscopy, Wiley, New York, 1975, p. 316.

(^27) T. C. Koopman,Physica, 1 , 104 (1933).