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The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 × 10⁻¹⁶ s. The frequency of revolution of the electron in its first excited state (in s⁻¹) is -

1. 1.6 × 10¹⁴
2. 5.6 × 10¹²
3. 6.2 × 10¹⁵
4. 7.8 × 10¹⁴

Correct answer: 7.8 × 10¹⁴

Solution

The frequency of revolution is inversely proportional to the time period of revolution. Since the time period for the ground state is known, we can calculate the time period for the first excited state, which is longer due to the electron being further from the nucleus, resulting in a lower frequency. The correct option reflects this calculation, yielding a frequency of 7.8 × 10¹⁴ s⁻¹.

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