Hydrogen ¹₁H, deuterium ²₁H, He⁺ and Li²⁺ each have one electron. For the transition n = 2→1, let the emitted wavelengths be λ₁, λ₂, λ₃ and λ₄, respectively. Which relation is correct?
Options

Question

Hydrogen ¹₁H, deuterium ²₁H, He⁺ and Li²⁺ each have one electron. For the transition n = 2→1, let the emitted wavelengths be λ₁, λ₂, λ₃ and λ₄, respectively. Which relation is correct?

Options

G1 Physics · Accepted Answer

For a hydrogen-like ion, transition energy for n=2→1 is proportional to the reduced mass μ and to Z². Hydrogen and deuterium differ only slightly because of reduced-mass correction, while He⁺ and Li²⁺ scale mainly as Z² = 4 and 9. Thus the wavelengths satisfy the relation listed in option A. Correct answer: A.