Question

If an electron in hydrogen atom jumps from 3^rd orbit to 2^nd orbit it emits a photon of wavelength λ. When it emits a photon from 4^th orbit to 3^rd orbit then the corresponding wavelength of emitted photon will be ______.

Options

• `16/25 lambda`

• `9/16 lambda`

• `20/7 lambda`

• `20/13 lambda`

Answer 1

If an electron in hydrogen atom jumps from 3^rd orbit to 2^nd orbit it emits a photon of wavelength λ. When it emits a photon from 4^th orbit to 3^rd orbit then the corresponding wavelength of emitted photon will be `bbunderline(20/7 lambda)`.

Explanation:

Using Bohr’s formula:

`1/lambda = R (1/n_1^2 - 1/n_2^2)`

For transition 3 → 2:

`1/lambda = R (1/2^2 - 1/3^2`

= `R (1/4 - 1/9)`

= `R * 5/36`

For transition 4 → 3:

`1/(lambda') = R (1/3^2 - 1/4^2)`

= `R (1/9 - 1/16)`

= `R * 7/144`

Taking ratio:

`(lambda')/lambda = (5//36)/(7//144)`

= `(5 xx 144)/(36 xx 7)`

= `20/7` λ