Question

Energy levels A, B, and C of an atom correspond to increasing values of energy i.e., \( E_A<E_B<E_C \). Let \( \lambda_1 \), \( \lambda_2 \), and \( \lambda_3 \) be the wavelengths of radiation corresponding to the transitions C to B, B to A, and C to A, respectively. The correct relation between \( \lambda_1 \), \( \lambda_2 \), and \( \lambda_3 \) is:

• A. \( \lambda_1^2 + \lambda_2^2 = \lambda_3^2 \)
• B. \( \frac{1}{\lambda_1} + \frac{1}{\lambda_2} = \frac{1}{\lambda_3} \)
• C. \( \lambda_1 + \lambda_2 + \lambda_3 = 0 \)
• D. \( \lambda_1 + \lambda_2 = \lambda_3 \)

Hint:

For transitions between energy levels, use the Rydberg formula to relate wavelengths to energy differences.

Answer 1

The Correct Option is B

Atomic transition radiation wavelengths are determined by the energy difference between energy levels. The Rydberg formula for transitions is given by: \[\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right),\] where \( R \) is the Rydberg constant, and \( n_1 \) and \( n_2 \) represent the principal quantum numbers of the initial and final states, respectively. For the transitions discussed, the relationship between wavelengths is: \[\frac{1}{\lambda_1} + \frac{1}{\lambda_2} = \frac{1}{\lambda_3}.\]