Hydrogen `(._(1)H^(1))`, Deuterium `(._(1)H^(2))`, singly ionised Helium `(._(2)H^(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 wave lengths of emitted radiation are `lambda_(1),lambda_(2),lambda_(3)` and `lambda_(4)` respectively then approximately which one of the following is correct?

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)`