An electron makes a transition from orbit `n = 4` to the orbit `n = 2` of a hydrogen atom. The wave number of the emitted radiations `(R =` Rydberg's constant) will be

Options

A. `(16)/(3R)`
B. `(16)/(5R)`
C. `(5R)/(16)`
D. `(3R)/(16)`

Answer

A

Explanation

Wavelength is give by
`" " (1)/(lambda)=R((1)/n_(2)^(2)-(1)/(n_(2)^(2)))rArr(1)/(lambda)=R [(1)/((2)^(2))-(1)/((4)^(2))]`
`rArr" " (1)/(lambda)=R((1)/(4)-(1)/(16))rArr(1)/(lambda)=R((4-1)/(16))`
`rArr" " (1)/(lambda)=(3R)/(16)rArrlambda=(16)/(3R)`