Question

Given below are two statements:
Statement I: When electric discharge is put on hydrogen, it emits discrete frequency in the electromagnetic spectrum.
Statement II: Frequency of He\(^+\) ion of 2\(^\text{nd}\) line of Balmer series is equal to first line of Lyman series.
In the light of the above statements, choose the correct option.

• A. Both statement I and statement II are correct.
• B. Both statement I and statement II are incorrect.
• C. Statement I is correct and statement II is incorrect.
• D. Statement I is incorrect and statement II is correct.

Hint:

The frequency of spectral lines can be derived from the Rydberg formula, where the difference in the inverse square of the integers determines the frequency of the emitted radiation.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
Statement I: When hydrogen is subjected to electric discharge, it emits discrete frequencies, which corresponds to the atomic spectral lines.
Statement II: The frequency of the 2nd line of the Balmer series for He\(^+\) ion is compared with the first line of the Lyman series for H atom. The frequencies of these lines are equal.
Step 2: Mathematical derivation.
For He\(^+\) ion: \[ v \propto \left( 2^2 - 1^2 \right) \propto 2^2 \left( \frac{1}{2^2} - \frac{1}{4^2} \right) \propto \frac{3}{4} \] For H atom: \[ v \propto \left( 1^2 - 1^2 \right) \propto 2^2 \left( \frac{1}{1^2} - \frac{1}{2^2} \right) \propto \frac{3}{4} \] Step 3: Conclusion.
Since the frequencies are the same for both the first line of the Lyman series and the 2nd line of the Balmer series, both statements are correct.