Question

Energy level A, B, C of a certain atom corresponds to increasing values of energy, i.e., $E_A<E_B<E_C.$

${\lambda }_1,{\lambda }_2,{\lambda }_3$ are the wavelengths of the radiation corresponding to the transitions C to B, B to A and C to A respectively. Which of the following statement(s) is/are correct?

• A. $\lambda ={\lambda }_1+{\lambda }_2$
• B. ${\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$
• C. ${\lambda }_1={\lambda }_2+{\lambda }_3=0$
• D. ${\lambda }_3^2={\lambda }_1^2+{\lambda }_2^2$

Answer 1

The correct option is B ${\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$

Given that:

$\Delta E_{AB}+\Delta E_{BC}=\Delta E_{CA}$

We know,
$E\propto \frac{1}{\lambda }$

$\frac{1}{{\lambda }_3}=\frac{1}{{\lambda }_2}+\frac{1}{{\lambda }_1}$

${\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$