Question

Ratio of wavelengths of first and third Lyman spectral lines of hydrogen atom is:

• A. 5:4
• B. 9:4
• C. 7:3
• D. 16:3

Hint:

Higher spectral lines correspond to shorter wavelengths.

Answer 1

The Correct Option is A

Step 1: Lyman series formula: \[ \frac{1}{\lambda} = R\left(1 - \frac{1}{n^2}\right) \]
Step 2: First line (n=2): \[ \frac{1}{\lambda_1} = R\left(1 - \frac{1}{4}\right) = \frac{3R}{4} \Rightarrow \lambda_1 \propto \frac{4}{3} \]
Step 3: Third line (n=4): \[ \frac{1}{\lambda_3} = R\left(1 - \frac{1}{16}\right) = \frac{15R}{16} \Rightarrow \lambda_3 \propto \frac{16}{15} \]
Step 4: Ratio: \[ \lambda_1 : \lambda_3 = \frac{4}{3} : \frac{16}{15} = \frac{4}{3} \times \frac{15}{16} = \frac{5}{4} \]