Hydrogen `(""_(1)H^(1))`, Deuterium `(""_(1)H^(2))`, single 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 wavelength of emitted radiation are `lamda_(1),lamda_(2),lamda_(3)` and `lamda_(4)` respectively then approximately which one of the following is corrent ?

Options

A. `lambda_(1) = lambda_(2) = 4lambda_(3) = 9lambda_(4)`
B. `lambda_(1) = 2lambda_(2) = 3lambda_(3) = 4lambda_(4)`
C. `4lambda_(1) = 2lambda_(2) = 2lambda_(3) = lambda_(4)`
D. `lambda_(1) = 2lambda_(2) = 2lambda_(3) = lambda_(4)`

Answer

A

Explanation

In Bohr model `1/lambda=Rz^(2)[1/n_(1)^(2)-1/n_(2)^(2)]implies z prop 1/z^(2)`
`lambda_(1) : lambda_(2) : lambda_(3) :lambda_(4) :: 1/1:1/1:1/4:1/9`
`implies lambda_(1)=lambda_(2)=4lambda_(3)=9lambda_(4)`