The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n=2 n=3 and n=4 n=6 transitions, respecti…

Question

The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n=2 n=3 and n=4 n=6 transitions, respectively, is:

1. A. 1/36
2. B. 1/16
3. C. 1/9
4. D. 1/4 (Correct answer)

Correct Answer

Option D — 1/4

Detailed Solution & Explanation

The correct answer is $\dfrac{1}{4}$.

Key Points

• $\dfrac{1}{\lambda}\propto\Delta E=R_H\left(\dfrac{1}{n_1^2}-\dfrac{1}{n_2^2}\right)$, so $\lambda\propto\dfrac{1}{\Delta E}$.
• $2\to3$: $\Delta E=R_H\left(\dfrac{1}{4}-\dfrac{1}{9}\right)=R_H\cdot\dfrac{5}{36}$.
• $4\to6$: $\Delta E=R_H\left(\dfrac{1}{16}-\dfrac{1}{36}\right)=R_H\cdot\dfrac{20}{576}$.
• $\dfrac{\lambda_{2\to3}}{\lambda_{4\to6}}=\dfrac{\Delta E_{4\to6}}{\Delta E_{2\to3}}=\dfrac{20/576}{5/36}=\dfrac{1}{4}$.