Hydrogen `(_(1)H^(1))` Deuterium `(_(1)H^(2))` singly omised helium `(_(1)He^(1))` and doubly ionised lithium `(_(1)Li^(6))^(++)` all have one electron around the nucleus Consider an electron transition from `n = 2 to n = 1` if the wavelength of emitted radiartion are `lambda_(1),lambda_(2), lambda_(3),and lambda_(4)`, repectivelly then approximetely which one of the following is correct ?

Options

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

Answer

A

Explanation

form `1/lambda=RZ^(2)(1/(1^(2))-1/(2^(2)))=3/4 RZ^(2) :. lambda=4/(3RZ^(2))`
`lambda_(1)=4/(2R)` , `lambda_(2)=4/(3R)` , `lambda_(3)=4/(3R(2^(2)))=4/(12R)` ,
`lambda_(4)=4/(3R(3^(2)))=4/(27R)` , `lambda_(1)=lambda_(2)= 4lambda_(3) =9lambda_(4)`.