Electron in hydrogen atom first jumps from third excited state to second excited state and then form second excited state to first excited state. The ratio of wavelength `lambda_(1): lambda_(2)` emitted in two cases is

Options

A. `(7)/(5)`
B. `(27)/(20)`
C. `(27)/(5)`
D. `(20)/(7)`

Explanation

`(1)/(lambda)=R[(1)/(n_(f)^(2))-(1)/(n_(i)^(2))]`
In first case, `n_(f)=3, n_(i)=4`
`therefore" "(1)/(lambda_(1))=R[(1)/(3^(2))-(1)/(4^(2))]=R[(1)/(9)-(1)/(16)]=(7)/(144)R" …(i)"`
In second case, `n_(f)=2, n_(i)=3`
`therefore" "(1)/(lambda_(2))=R[(1)/(2^(2))-(1)/(3^(2))]=R[(1)/(4)-(1)/(9)]=(5)/(36)R" ...(ii)"`
Divide (ii) by (i), we get
`(lambda_(1))/(lambda_(2))=(5)/(36)xx(144)/(7)=(20)/(7)`