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The ratio of temperatures T₁/T₂ is proportional to the cube of the ratio of principal quantum numbers n₁/n₂. If n₁ = 2n₂, find the ratio T₁/T₂.

1. T₁/T₂ ∝ n₁²/n₂²
2. T₁/T₂ ∝ n₁³/n₂³
3. T₁/T₂ ∝ n₁/n₂
4. T₁/T₂ ∝ n₁⁴/n₂⁴

Correct answer: T₁/T₂ ∝ n₁³/n₂³

Solution

The problem states that T₁/T₂ is proportional to the cube of the ratio of n₁/n₂. Substituting n₁ = 2n₂, we get (n₁/n₂)³ = (2n₂/n₂)³ = 2³ = 8. Thus, T₁/T₂ ∝ n₁³/n₂³.

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