Question

Let the series limit for Balmer series be \( \lambda_1 \) and the longest wavelength for Brackett series be \( \lambda_2 \). Then \( \lambda_1 \) and \( \lambda_2 \) are related as

• A. \( \lambda_2 = 0.09 \lambda_1 \)
• B. \( \lambda_1 = 0.09 \lambda_2 \)
• C. \( \lambda_1 = 1.11 \lambda_2 \)
• D. \( \lambda_2 = 1.11 \lambda_1 \)

Hint:

The wavelength of the series limit is shorter for transitions involving higher principal quantum numbers.

Answer 1

The Correct Option is B

Step 1: Understanding the series limits.
The series limit for the Balmer series corresponds to the wavelength when the electron jumps from the \( n = \infty \) level to \( n = 2 \). The series limit for the Brackett series corresponds to the transition from \( n = \infty \) to \( n = 4 \).
Step 2: Using the relationship for wavelengths.
The relation between the wavelengths for the two series is given by: \[ \lambda_1 = 0.09 \lambda_2 \] Step 3: Conclusion.
The correct answer is (B), \( \lambda_1 = 0.09 \lambda_2 \).