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What is the kinetic energy of an electron in the second Bohr orbit of a hydrogen atom, taking a₀ as the Bohr radius?

1. h² / 4π²mₑa₀²
2. h² / 16π²mₑa₀²
3. h² / 32π²mₑa₀²
4. h² / 64π²mₑa₀²

Correct answer: h² / 32π²mₑa₀²

Solution

The kinetic energy of an electron in the Bohr model is derived from its orbital radius and the quantization of angular momentum. In the second orbit, the radius is twice that of the first, leading to the specific factor of 1/32 in the kinetic energy formula.

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