Question

The energy levels in an atom $A,B$ and $C$ are in increasing order $E_{A} < E_{B} < E_{C}$ . The x-rays emitted in transitions $C \rightarrow B,B \rightarrow A$ and $C \rightarrow A$ , have wavelengths $\lambda _{1},\lambda _{2}$ and $\lambda _{3}$ then which of the following relation is true?

• 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. none

Answer 1

Answer: (B)

As $E_{A} < E_{B} < E_{C}$
Therefore C is higher energy level & A is at lowest
$E_{C \rightarrow A}=E_{C \rightarrow B}+E_{B \rightarrow A}$
$\frac{h c}{\lambda _{3}}=\frac{h c}{\lambda _{1}}+\frac{h c}{\lambda _{2}}$
therefore
$\lambda _{3}=\frac{\lambda _{1} \lambda _{2}}{\lambda _{1} + \lambda _{2}}$