Question

The wave number of the first emission line in the Balmer series of H-Spectrum is: \[ (R = \text{Rydberg constant}) \]

• A. \( \frac{5}{36} R \)
• B. \( \frac{9}{400} R \)
• C. \( \frac{7}{6} R \)
• D. \( \frac{3}{4} R \)

Hint:

The wave number for the first line of the Balmer series in the hydrogen spectrum is derived from the Rydberg formula.

Answer 1

The Correct Option is A

Step 1: Balmer Series Formula.
The wavelength for the first emission line in the Balmer series is given by the Rydberg formula: \[ \frac{1}{\lambda} = R \left( \frac{1}{2^2} - \frac{1}{n^2} \right) \] For the first emission line, \( n = 3 \). The wave number \( \nu \) is \( \frac{1}{\lambda} \), and the wave number for the first emission line is \( \frac{5}{36} R \).
Step 2: Conclusion.
The correct answer is (A), \( \frac{5}{36} R \).