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. 20/7
B. `7//5`
C. 27/20
D. 27/5

Answer

D

Explanation

For the transition between `n_2`=3 and `n_1`=2
`1/lambda_1=R(1/2^2-1/3^2)=R((9-4)/36)=(5R)/(36)`
`lambda_1=36/(5R)` …(i)
For the transition between `n_2`=2 and `n_1`=1
`1/lambda_2=R(1/1^2-1/2^2)=3/(4R)`
`lambda_2=4/(3R)`….(ii)
From equation (i) by (ii)
`lambda_1/lambda_2=36/(5R)xx(3R)/4=(24R)/5`