Question

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?

• A. III
• B. IV
• C. I
• D. II

Answer 1

Answer: (A)

Energy of emitted radiation E$=Rhc[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$
$R_{(4\to 3)}=Rhc[\frac{1}{3^2}-\frac{1}{4^2}]$
$=Rhc\left[\frac{7}{9\times 16}\right]=0.05Rhc$
$E_{(4\to 2)}=Rhc[\frac{1}{2^2}-\frac{1}{4^2}]$
$=Rhc\left[\frac{3}{16}\right]=0.2Rhc$
$E_{(2\to 1)}=Rhc[\frac{1}{(1{)}^2}-\frac{1}{(2{)}^2}]$
$=Rhc\left[\frac{3}{4}\right]=0.75Rhc$
$E_{(1\to 4)}=Rhc[\frac{1}{(4{)}^2}-\frac{1}{(1{)}^2}]$
$=-\frac{8}{9}Rhc=-0.9Rhc$
Thus, transition III gives most energy.