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)

$\frac{1}{\lambda }=R{\left(1\right)}^2\left(\frac{1}{2^2}-\frac{1}{3^2}\right)$
$\frac{1}{{\lambda }_2}=R{\left(1\right)}^2\left(\frac{1}{3^2}-\frac{1}{4^2}\right)$
$\frac{\frac{1}{\lambda }}{\frac{1}{{\lambda }_2}}=\frac{\frac{1}{4}-\frac{1}{9}}{\frac{1}{9}-\frac{1}{16}}=\frac{\frac{5}{4\times 9}}{\frac{16-9}{9\times 16}}$
$\frac{{\lambda }_2}{\lambda }=\frac{5}{4\times 9}\times \frac{9\times 16}{7}=\frac{20}{7}$
${\lambda }_2=\frac{20}{7}\lambda$