Chapter 6, Problem 37P

Interpretation Introduction

Interpretation: The quantitative energy level diagram for molecular orbital of ${\text{N}}_{\text{2}}$ electrons should be determined.

Concept introduction: In photoelectron spectroscopy (PES), sample with high-frequency radiation is illuminated and kinetic energy of photoelectrons emitted from sample is measured. Also, photoelectron spectroscopy gives MO description of bonding and measure energy for individual MO in molecules. For, example, a diatomic gaseous molecule that has energy of $21.2\text{2 eV}$ is illuminated to measure the kinetic energy of emitted photoelectrons. The photoelectron spectroscopy spectrum then shows a series of peaks. The ionization energy is measured that is required to liberate electrons contribute to peak in spectrum.

Ionization energy is difference of kinetic energy of electrons from the energy of photon.

The formula to calculate ionization energy $\left(IE\right)$ is as follows:

  $IE=h{\nu }_{\text{photon}}-\frac{1}{2}{m}_e{\nu }^2$

Where,

• $h{\nu }_{\text{photon}}$ is the energy of electrons.
• $\frac{1}{2}{m}_e{\nu }^2$ is kinetic energy of electrons.

The measured ionization energy is negative of the energy of orbital from which photoelectrons were emitted.