Question

In a hydrogen atom, the frequency of the photon emitted when an electron jumps from the second orbit to the first orbit is 'f'. The frequency of the photon emitted when an electron jumps from the third excited state to the first excited state is:

• A. \( \frac{f}{2} \)
• B. \( \frac{f}{4} \)
• C. \( \frac{f}{8} \)
• D. \( f \)

Hint:

Remember, the frequency of emitted photons is higher for transitions to lower energy levels.

Answer 1

The Correct Option is B

Using the Rydberg formula for the frequencies of lines in the hydrogen spectrum: \[ f = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \] For a jump from the third excited state (n=4) to the first excited state (n=2), the frequency is: \[ f = R \left( \frac{1}{2^2} - \frac{1}{4^2} \right) = R \left( \frac{1}{4} - \frac{1}{16} \right) = R \left( \frac{3}{16} \right) \] Comparing this with the frequency for the transition from the second orbit to the first, which is based on \( n_1 = 1, n_2 = 2 \), we find the ratio is \( \frac{1}{4} \).