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)

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