Question

If an electron in hydrogen atom jumps from an orbit of level \( n = 3 \) to an orbit at level \( n = 2 \), emitted radiation has a frequency of
\( (R = \text{Rydberg’s constant}, \ c = \text{speed of light}) \)

• A. \( \frac{3Rc}{27} \)
• B. \( \frac{Rc}{25} \)
• C. \( \frac{8Rc}{9} \)
• D. \( \frac{5Rc}{36} \)

Hint:

Always use \( \nu = Rc \left( \frac{1}{n_2^2} - \frac{1}{n_1^2} \right) \) for hydrogen spectrum transitions.

Answer 1

The Correct Option is D

For hydrogen atom transitions, the frequency of emitted radiation is given by: \[ \nu = Rc \left( \frac{1}{n_2^2} - \frac{1}{n_1^2} \right) \] Substitute: \( n_1 = 3, \quad n_2 = 2 \Rightarrow \nu = Rc \left( \frac{1}{2^2} - \frac{1}{3^2} \right) = Rc \left( \frac{1}{4} - \frac{1}{9} \right) = Rc \left( \frac{9 - 4}{36} \right) = \frac{5Rc}{36} \)