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Energy levels A, B, C of a certain atom correspond to increasing values of energy i.e., E₄ < E₃ < E₂. λ₁, λ₂, λ₃ are the wavelengths of radiation corresponding to the transitions C to B, B to A and C to A respectively, which of the following relation is correct?

1. λ₃ = λ₁ + λ₂
2. λ₃ = λ₁λ₂ / (λ₁ + λ₂)
3. λ₁ + λ₂ + λ₃ = 0
4. λ₃² = λ₁² + λ₂²

Correct answer: λ₃ = λ₁λ₂ / (λ₁ + λ₂)

Solution

The energy difference for the transition C to A is the sum of the energy differences for transitions C to B and B to A. Using the relation E = hc/λ, the reciprocal of the wavelength for C to A is the sum of the reciprocals of the wavelengths for C to B and B to A. This leads to the formula λ₃ = λ₁λ₂ / (λ₁ + λ₂).

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