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

Answer

B

Explanation

Wavelength of emitted radian by the transition of electron from `.n_(i).` orbit to `.n_(k).` orbit,
`(1)/(lamda_(ik))=RZ^(2)[(1)/(n_(k)2)-(1)/(n_(i)2)]`
here R and `n_(k),n_(i)` are constant,
`:.lamda_(ik)prop(1)/(Z^(2))`
`:.lamda_(1):lamda_(2):lamda_(3):lamda_(4)=(1)/((1)^(2)):(1)/((1)^(2)):(1)/((2)^(2)):(1)/((3)^(2))`
`=(1)/(1):(1)/(1):(1)/(4):(1)/(9)`
`:.lamda_(1):lamda_(2)=1:1`
`:.lamda_(1)=lamda_(2)`
`lamda_(1):lamda_(3)=1:(1)/(4)`
`:.(lamda_(1))/(lamda_(3))=(1)/((1)/(4))implieslamda_(1)=4lamda_(3)`
and `lamda_(1):lamda_(4)=1:(1)/((1)/(9))`
`:.(lamda_(1))/(lamda_(4))=(1)/((1)/(9))implieslamda_(1)=9lamda_(4)`
`:.lamda_(1)=lamda_(2)=4lamda_(3)=9lamda_(4)`