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 wavelength \( \lambda_1 : \lambda_2 \) emitted in the two cases is:

• A. 7/5
• B. 27/20
• C. 27/5
• D. 20/7

Hint:

The wavelength ratio for electron transitions in hydrogen can be derived from the Rydberg formula, considering the energy difference between the levels involved.

Answer 1

The Correct Option is D

Step 1: The wavelengths of emitted radiation during electron transitions in hydrogen atoms can be calculated using the Rydberg formula for the emission spectrum.
Step 2: The wavelengths \( \lambda_1 \) and \( \lambda_2 \) correspond to the transitions from the third to the second excited state and from the second to the first excited state, respectively. The ratio of these wavelengths comes out to be \( 20/7 \).

Final Answer: \[ \boxed{\dfrac{20}{7}} \]