Hydrogen `(H)`, deuterium `(D)`, singly ionized helium `(He^(+))` and doubly ionized lithium `(Li)` all have one electron around the nucleus. Consider `n = 2` to `n = 1` transition. The wavelength of emitted radiations are `lambda_(1), lambda_(2), lambda_(3)` and `lambda_(4)` respectively. then approximately

Options

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

Answer

A

Explanation

Using `DeltaE prop Z^(2) ( :. n_(1)` and `n_(2)` are same)
`rArr (hc)/(lambda) prop Z^(2) rArr lambda Z^(2) =` constant
`rArr lambda_(1) Z_(1)^(2) = lambda_(2) Z_(2)^(2) = lambda_(3) Z_(3)^(2) = lambda_(4) Z_(4)^(2)`
`rArr lambda_(1) xx 1 = lambda_(2) xx 1^(2) = lambda_(3) xx 2^(2) = lambda_(3) xx 3^(3)`
`rArr lambda_(1) = lambda_(2) 4 lambda_(3) = 9 lambda_(4)`