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For large quantum numbers (n >> 1), what is the dependence of the frequency of the photon emitted when an electron in a hydrogen atom transitions from the nth orbit to the (n-1)th orbit?

1. nu ∝ 1/n
2. nu ∝ 1/n²
3. nu ∝ 1/n³
4. nu ∝ 1/n⁴

Correct answer: nu ∝ 1/n³

Solution

For large n, expanding 1/(n-1)² ≈ 1/n² + 2/n³ gives h*nu ≈ 13.6 * (2/n³), so nu ∝ 1/n³.

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