Q: Hydrogen (_{1}H^{1}), Deuterium (_{1}H^{2}), singly ionised Helium (_{2}He^{4})+ and doubly ionised lithium (_{3}Li^{6})++ all have one electron around the nucleus. Consider an electron transition from n = 2 to n = 1. If the wavelengths of emitted radiation are λ1, λ2, λ3 and λ4 respectively then approximately which one of the following is correct

(a) 4λ_{1} = 2λ_{2} = 2λ_{3} = λ_{4}

(b) λ_{1} = 2λ_{2} = 2λ_{3} = λ_{4}

(c)λ_{1} = λ_{2} = 4λ_{3} = 9λ_{4}

(d) λ_{1} = 2λ_{2} = 3λ_{3} = 4λ_{4}

Ans: (c)

Sol: $\frac{1}{\lambda} \propto Z^2 $

$ \lambda \propto \frac{1}{Z^2} $

$ \lambda_1 : \lambda_2 : \lambda_3 : \lambda_4 = \frac{1}{1^2} : \frac{1}{1^2} : \frac{1}{2^2} : \frac{1}{3^2}$

$ \lambda_1 : \lambda_2 : \lambda_3 : \lambda_4 = 1 : 1 : \frac{1}{4} : \frac{1}{9}$

λ_{1} = λ_{2} = 4λ_{3} = 9λ_{4}