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)

$E=Rhc\left[\frac{1}{n^{2}_{1}}-\frac{1}{n^{2}_{2}}\right]$
$E_{\left(4 \to3\right)}=Rhc\left[\frac{1}{3^{2}}-\frac{1}{4^{2}}\right]$
$=Rhc\left[\frac{7}{9\times16}\right]=0.05\,Rhc$
$E_{\left(4 \to2\right)}=Rhc\left[\frac{1}{2^{2}}-\frac{1}{4^{2}}\right]$
$=Rhc\left[\frac{3}{16}\right]=0.2\,Rhc$
$E_{\left(2 \to1\right)}=Rhc\left[\frac{1}{\left(1\right)^{2}}-\frac{1}{\left(2\right)^{2}}\right]$
$=Rhc\left[\frac{3}{4}\right]=0.75\,Rhc$
$E_{\left(1 \to3\right)}=Rhc\left[\frac{1}{\left(3\right)^{2}}-\frac{1}{\left(1\right)^{2}}\right]$
$=-\frac{8}{9}Rhc=-0.9\,Rhc$
Thus, transition $III$ gives most energy. Transition $I$ represents the absorption of energy.