If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength `lambda`. When it jumps from the `4^(th)` orbit to the `3^(rd)` orbit, the corresponding wavelength of the photon will be

Options

A. `(20)/(7) lambda`
B. `(20)/(13) lambda`
C. `(16)/(25) lambda`
D. `(9)/(16) lambda`

Answer

A

Explanation

Wavelength of photon when electron makes transition from third orbit to second orbit
`(1)/(lambda)=R((1)/(2^(2))-(1)/(3^(2)))...(1)`
Wavelength of photon when electron makes transition from forth orbit to third orbit
`(1)/(lambda.)=R((1)/(3^(2))-(1)/(4^(2)))...(2)`
by taking ratio of (1) and (2)
`(lambda.)/(lambda)=((1)/(4)-(1)/(9))/((1)/(9)-(1)/(16))=((5)/(36))/((7)/(144))=(20)/(7)`
`:. lambda.=(20)/(7) lambda`