Chapter 8, Problem 8C.10P

(a)

Interpretation Introduction

Interpretation:

The splitting in ${\text{cm}}^{-1}$ between the three spectral lines for a transition between a ${}^1{\text{S}}_0$ term and a ${}^1{\text{P}}_1$ term in the presence of a magnetic field of $2\text{T}$ has to be calculated.

Concept introduction:

Stern and Gerlach performed an experiment in which a beam of silver atoms was passed through a magnetic field.  They observed that the beam of silver atoms was splitted in two different beams.  The experiment helped to discover the spin of the electron.  Zeeman Effect is the splitting of spectral lines in the presence of external magnetic field.

(b)

Interpretation Introduction

Interpretation:

The value of the splitting in ${\text{cm}}^{-1}$ between the three spectral lines for a transition between a ${}^1{\text{S}}_0$ term and a ${}^1{\text{P}}_1$ term in the presence of a magnetic field of $2\text{T}$ has to be compared with typical optical transition wavenumbers.  The line spitting occurred by the normal Zeeman Effect is relatively small or relatively large has to be predicted.

Concept introduction:

Rydberg equation is used to represent the wavenumber or wavelength of the lines present in the atomic spectrum of an element.  The Rydberg equation for the hydrogen atom is given by the expression as shown below.

    $\tilde{v}=R_{\text{H}}\left(\frac{1}{n_{\text{1}}^2}-\frac{1}{n_{\text{2}}^2}\right)$