Question

If the wavelength of the first member of the Lyman series of hydrogen is \( \lambda \). The wavelength of the second member will be:

• A. \( \frac{27}{32} \lambda \)
• B. \( \frac{32}{27} \lambda \)
• C. \( \frac{27}{5} \lambda \)
• D. \( \frac{5}{27} \lambda \)

Answer 1

The Correct Option is A

For the first member of the Lyman series:

\[ \frac{1}{\lambda} = \frac{13.6 \, z^2}{hc} \left[ \frac{1}{1^2} - \frac{1}{2^2} \right] \quad \dots \text{(i)} \]

For the second member of the Lyman series:

\[ \frac{1}{\lambda'} = \frac{13.6 \, z^2}{hc} \left[ \frac{1}{1^2} - \frac{1}{3^2} \right] \quad \dots \text{(ii)} \]

Dividing equation (i) by (ii):

\[ \lambda' = \frac{27}{32} \lambda \]