Question

When the electron in the hydrogen atom jumps from 2^nd orbit to 1^st orbit, the wavelength of radiation emitted is λ. When the electrons jump from 3^rd orbit to 1^st orbit, the wavelength of emitted radiation would be.

• A. $\frac{27}{32}\lambda$
• B. $\frac{32}{27}\lambda$
• C. $\frac{2}{3}\lambda$
• D. $\frac{3}{2}\lambda$

Answer 1

Answer: (A)

$\frac{27}{32}\lambda$

Answer 2

$\frac{1}{\lambda} = R\left\lbrack \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right\rbrack$

First condition $\frac{1}{\lambda} = R\left\lbrack \frac{1}{1^{2}} - \frac{1}{2^{2}} \right\rbrack \Rightarrow R = \frac{4}{3\lambda}$

Second condition $\frac{1}{\lambda'} = R\left\lbrack \frac{1}{1^{2}} - \frac{1}{3^{2}} \right\rbrack$

$\Rightarrow \lambda' = \frac{9}{8R} \Rightarrow \lambda' = \frac{9}{8 \times \frac{4}{3\lambda}} = \frac{27\lambda}{32}$.