Hydrogen (1H1), Deuterium (1H2), singly ionised Helium (2He4)+ and doubly ionised lithium (3Li6)+ all have one electron around the nucleus. Consider an electron transition from n = 2 to n = 1. If the wave lengths of emitted radiation are λ1, λ2, λ3 and λ4 respectively then approximately which one of the following is correct?

Engineering

Physics

Spectrum of Hydrogen and Hydrogen Like Atoms

Question

Hydrogen (₁H¹), Deuterium (₁H²), singly ionised Helium (₂He⁴)⁺ and doubly ionised lithium (₃Li⁶)⁺ all have one electron around the nucleus. Consider an electron transition from n = 2 to n = 1. If the wave lengths of emitted radiation are λ₁, λ₂, λ₃ and λ₄ respectively then approximately which one of the following is correct?

λ₁ = 2λ₂ = 3λ₃ = 4λ₄

λ₁ = λ₂ = 4λ₃ = 9λ₄

4λ₁ = 2λ₂ = 2λ₃ = λ₄

λ₁ = 2λ₂ = 2λ₃ = λ₄

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$\frac{1}{λ} = {RZ}^{2} \times \frac{3}{4}$

$\frac{1}{λ_{1}} = \frac{3 R}{4}$

$λ_{1} = \frac{4}{3 R} = λ_{2}$

$λ_{3} = \frac{4}{3 R \times 4} = \frac{λ_{2}}{4}$

$λ_{4} = \frac{4}{3 R \times 9} = \frac{λ_{1}}{9}$