Q: 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 wavelengths of emitted radiation are λ1, λ2, λ3 and λ4 respectively then approximately which one of the following is correct
(a) 4λ1 = 2λ2 = 2λ3 = λ4
(b) λ1 = 2λ2 = 2λ3 = λ4
(c)λ1 = λ2 = 4λ3 = 9λ4
(d) λ1 = 2λ2 = 3λ3 = 4λ4
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}$
λ1 = λ2 = 4λ3 = 9λ4