Question

Hydrogen (\(^1_1H\)); deuterium \((^2_1 )H\), singly ionised helium \((^4_2 H)\) and doubly ionised lithium \((^8_2 Li)^{++}\) , all have only one electron orbiting around the nucleus. Consider an electron transition from n = 2 to n = 1. If the wavelengths emitted are λ₁ , λ₂ , λ₃ and λ₄ ,

(1) 4λ₁ = 2λ₂ = 2λ₃ = λ₄

(2) λ₁ = 2λ₂ = 2λ₃ = λ₄

(3) λ₁ = λ₂ = 4λ₃ = 9λ₄

(4) λ₁ = 2λ₂ = 3λ₃ = 4λ₄

Answer 1

(3) λ₁ = λ₂ = 4λ₃ = 9λ₄

For a hydrogen like atom, of atomic number z; for the given transition, we have

Here R is Rydberg’s constant, for hydrogen. For the given four atoms z₁ = 1, z₂ = 1, z₃ = 2, and z₄ = 3. 

Therefore,