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$=Rhc \bigg [\frac {1}{n_1^2}- \frac {1}{n_2^2}\bigg ]$
$ R_{(4\rightarrow 3)}=Rhc \bigg [\frac {1}{3^2}- \frac {1}{4^2}\bigg ]$
$ =Rhc \bigg [\frac {7}{9 \times 16}\bigg ]=0.05 \, Rhc $
$ E_{(4 \rightarrow2)}=Rhc \bigg [\frac {1}{2^2}- \frac {1}{4^2}\bigg ]$
$ =Rhc \bigg [\frac {3}{16}\bigg ]=0.2 Rhc$
$ E_{(2 \rightarrow 1)}=Rhc \bigg [\frac {1}{(1)^2}- \frac {1}{(2)^2} \bigg ] $
$ =Rhc\bigg [\frac {3}{4}\bigg ]=0.75 Rhc$
$ E_{(1 \rightarrow4)}=Rhc \bigg [\frac {1}{(4)^2}- \frac {1}{(1)^2}\bigg ]$
$ =- \frac {8}{9}Rhc=-0.9Rhc$
Thus, transition III gives most energy.