Question

Energy levels $A, B$ and $C$ of a certain atom corresponding to increasing values of energy i.e. $E_{A}

• A. $\lambda_1 + \lambda_2 + \lambda_3 = 0$
• B. $\lambda_3^2 = \lambda^2_1 + \lambda_2^2 $
• C. $\lambda_3 = \lambda_1 + \lambda_2 $
• D. $\lambda_3 = \frac{\lambda_1 \lambda_2}{\lambda_1 + \lambda_2}$

Answer 1

Answer: (D)

As $E_C - E_A = E_C - E_B + E_B - E_A$
$\frac{hc}{\lambda_{3}} =\frac{hc}{\lambda_{1}}+\frac{hc}{\lambda_{2}}$
$\frac{1}{\lambda_{3}} =\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}}$
$ \therefore \:\:\:\: \lambda_3 = \frac{\lambda_1 \lambda_2}{\lambda_1 + \lambda_2}$