Question

Energy levels, A, B, C of a certain atom correspond 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 corresponding to the transitions C to B, B to A and C to A respectively, which of the following relations 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. ${\lambda }_3^3={\lambda }_1^2+{\lambda }_2^2$

Answer 1

Answer: (B)

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

As energy emitted varies inversely as wavelength, therefore
$\frac{1}{{\lambda }_3}=\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}=\frac{{\lambda }_2+{\lambda }_1}{{\lambda }_1{\lambda }_2}\Rightarrow {\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$