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 $C\to B,B\to A$ and $C\to A$ , 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
$E_{C\to A}=E_{C\to B}+E_{B\to A}$
$\frac{hc}{{\lambda }_3}=\frac{hc}{{\lambda }_1}+\frac{hc}{{\lambda }_2}$
therefore
${\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$