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← JEE Main 2014 · 6 Apr · Shift 1
PhysicsSingle correct+4 / -1Question 27 of 90

JEE Main 2014 · 6 Apr · Shift 1, Physics question 27

Hydrogen (1H1)\left({}_1\mathrm H^1\right), Deuterium (1H2)\left({}_1\mathrm H^2\right), singly ionised Helium (2He4)+\left({}_2\mathrm{He}^4\right)^+ and doubly ionised lithium (3Li6)++\left({}_3\mathrm{Li}^6\right)^{++} all have one electron around the nucleus. Consider an electron transition from n=2n=2 to n=1n=1. If the wave lengths of emitted radiation are λ1\lambda_1, λ2\lambda_2, λ3\lambda_3 and λ4\lambda_4 respectively then approximately which one of the following is correct ?

Choose one option
Answer and worked solution

Official answer: C

1λ∝Z2\dfrac1\lambda\propto Z^2 for the same transition (ignoring the small reduced-mass difference between H and D). With Z=1,1,2,3Z=1,1,2,3:
λ1=λ2=4λ3=9λ4.\lambda_1=\lambda_2=4\lambda_3=9\lambda_4.