Hydrogen `(`1`H^(1))` Deuterium `(`1`H^(2))` singly ionized helium `(`2`He^())^+` and doubly ionized 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 `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 .