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For a hydrogen-like ion Li2+ (atomic number Z = 3), given that n1 + n2 = 4 and n2 - n1 = 2 (where n1 and n2 are the lower and upper energy levels respectively), find the wavelength of the photon emitted in the transition n2 -> n1 in nanometres. Express the answer as the sum of its digits. (Given: Rydberg constant R_H = 10⁷ m⁻¹.)

1. 6
2. 7
3. 8
4. 9

Correct answer: 8

Solution

n1 = 1, n2 = 3; 1/lambda = 10⁷ * 9 * (1 - 1/9) = 8 * 10⁷ m⁻¹, so lambda = 12.5 nm. Sum of digits of 12.5: 1 + 2 + 5 = 8.

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