Question

If an electron in a hydrogen atom jumps from the $3^{rd}$ orbit to the $2^{nd}$ orbit, it emits a photon of wavelength $\lambda$. When it jumps from the $4^{th}$ orbit to the $3^{rd}$ orbit, the corresponding wavelength of the photon will be

• A. $\frac{16}{25} \lambda$
• B. $\frac{9}{16} \lambda$
• C. $\frac{20}{7} \lambda$
• D. $\frac{20}{13} \lambda$

Answer 1

Answer: (C)

$\frac{1}{\lambda } =R \left(1\right)^{2} \left(\frac{1}{2^{2}} - \frac{1}{3^{2}}\right) $
$ \frac{1}{\lambda _{2}} =R\left(1\right)^{2} \left(\frac{1}{3^{2} } - \frac{1}{4^{2}}\right) $
$ \frac{\frac{1}{\lambda }}{\frac{1}{\lambda _{2}}} = \frac{\frac{1}{4} - \frac{1}{9}}{\frac{1}{9}-\frac{1}{16}} = \frac{\frac{5}{4\times9}}{\frac{16-9}{9\times16}} $
$ \frac{\lambda _{2} }{\lambda } = \frac{5}{4\times9} \times\frac{9 \times16}{7} = \frac{20}{7} $
$ \lambda _{2} = \frac{20}{7} \lambda $