Question

A hydrogen atom emits a photon of wavelength λ , in returning from the first excited state to ground state. Another hydrogen like ion of an atomic number z, emits a photon of wavelength (α λ) ; in returning from its second excited state to its first excited state. The value of z, then equals

(1) \(\sqrt{\frac{3}{5α}}\) 

(2) \(\sqrt{\frac{9}{2α}}\)

(3) \(\sqrt{\frac{27}{5α}}\)

(4) \(\sqrt{\frac{5}{27α}}\)

Answer 1

 (3) \(\sqrt{\frac{27}{5α}}\)

For hydrogen atom, the given transition, corresponds to an electron moving from n₂ = 2, to n₁ = 1. Therefore,

For the given ion; the electron jumps from n₂ = 3, to n₁ = 2. Therefore,

From equations (1) and (2), we have