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

Answer

C

Explanation

`(1)/(lambda)=RZ^(2)((1)/(1^(2))-(1)/(2^(2)))`
`" " (1)/(lambda_(1))=R(1)^(2)(3//4),(1)/(lambda_(2))=R(1)^(2)(3//4)`
`" " (1)/(lambda_(3))=R(2)^(2)(3//4),(1)/(lambda_(4))=R3^(2)(3//4)`
`" " (1)/(lambda_(1))=(1)/(4lambda_(3))=(1)/(9lambda_(4))=(1)/(lambda_(2))`
So, option (c) is correct .