Question

Energy levels A, B , C of a certain atom corrrespond to increasing values of energy , i.e , $E_A<E_B<E_C$ . If ${\lambda }_1,{\lambda }_2,{\lambda }_3$ are the wavelengths of radiations for the transitions $C\to B,B\to A$ and $C\to A$ respectively then which of the following statements 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. ${\lambda }_3^0={\lambda }_1^2+{\lambda }_2^2$

Answer 1

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

The sum of the energies for the transitions C to B and B to A is equal to the energy for transition C to A. In other words, the energies and frequencies are additive whereas wavelength is inversely proportional to the frequency, so the reciprocals of the wavelengths are additive.

Thus,

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

or

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