Question

Energy levels A,B and C of a certain atom correspond to increasing values of energy i.e., EA<EB<EC. If $\lambda_1,\lambda_2$ and $\lambda_3$ are wavelengths of radiations corresponding to transitions C to B,B to A and C to A respectively, which of the following relations is correct ?

• A. $\lambda_3$ = $\lambda_1+\lambda_2$
• B. $\lambda_3$ = $\frac{\lambda_1 \lambda_2}{\lambda_1+ \lambda_2}$
• C. \lambda_1+\lambda_2$$+\lambda_3 = 0
• D. $\lambda_{23}$ = $\lambda_{21}+\lambda_{22}$

Answer 1

Answer: (B)

$\lambda_3$ = $\frac{\lambda_1 \lambda_2}{\lambda_1+ \lambda_2}$

Answer 2

We Know
E=hν=$\frac{hc}{\lambda}$

Energy corresponding to transition EC$\rightarrow$EB=$\frac{hc}{\lambda_1}$
Energy corresponding to transition EC$\rightarrow$EA=$\frac{hc}{\lambda_3}$
Energy corresponding to transition EB$\rightarrow$EA=$\frac{hc}{\lambda_2}$

Since $\frac{hc}{\lambda_3}$=$\frac{hc}{\lambda_1}$+$\frac{hc}{\lambda_2}$
$\Rightarrow$ $\lambda_3$ = $\frac{\lambda_1 \lambda_2}{\lambda_1+ \lambda_2}$

Therefore, the correct option is (B): $\lambda_3$ = $\frac{\lambda_1 \lambda_2}{\lambda_1+ \lambda_2}$