Question

Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state.
The ratio of the wavelengths $\lambda_1 : \lambda_2$ emitted in the two cases is:

• A. $\frac{7}{5}$
• B. $\frac{27}{20}$
• C. $\frac{27}{5}$
• D. $\frac{20}{7}$

Answer 1

Answer: (D)

$\frac{20}{7}$

Answer 2

Wavelength observed from transition of $n_{i}$ to $n_{f}$ is
$\lambda=\frac{1}{\left[\frac{1}{n_{f}{ }^{2}}-\frac{1}{n_{i}{ }^{2}}\right]}$
For $\lambda_{1}, n _{ i }=4, n _{ f }=3$
For $\lambda_{2}, n _{ i }=3, n _{ f }=2$
We get $\lambda_{1:} \lambda_{2}=20: 7$