What is the frequency in Hz of emitted radiation when an electron jumps from fourth orbit to secondth orbit in a hydrogen atom ?
[Where `R=10^(5)cm^(-1)` ]

Options

A. `(3)/(4)xx10^(15)`
B. `(3)/(16)xx10^(15)`
C. `(9)/(16)xx10^(15)`
D. `(3)/(8)xx10^(15)`

Answer

C

Explanation

`(1)/(lamda_(ik))=R((1)/(n_(k)^(2))-(1)/(n_(i)^(2)))`
`=10^(5)((1)/(2^(2))-(1)/(4^(2)))" "( :.R=10^(5)cm^(-1))`
`=10^(5)((1)/(4)-(1)/(16))`
`=10^(5)((4-1)/(16))`
`(1)/(lamda_(ik))=10^(5)xx(3)/(16)`
but `c=3xx10^(10)cm//s`
`(c)/(lamda_(ik))=(3xx10^(10)xx10^(5)xx3)/(16)`
`:.f_(ik)=(9)/(16)xx10^(15)Hz`