An electron in the hydrogen atom absorbs energy and jumps to the 4th orbit. It jumps back to the ground state in steps e.g., from 4th to 3rd orbit, then from 3rd to 2nd orbit and finally to the ground state etc.
If `lambda_(1)` is the wave length of line for jump of the electron from 4th to 3rd orbit and `lambda_(2)` that of the line for jump from 3rd to 2nd orbit, then wavelength of the line for jump from 4th orbit to 2nd orbit would be

Options

A. `lambda_(1)+lambda_(2)`
B. `(lambda_(1) lambda_(2))/(lambda_(1)+lambda_(2))`
C. `(lambda_(1) lambda_(2))/(lambda_(1)-lambda_(2))`
D. `(lambda_(1)+ lambda_(2))/(lambda_(1)+lambda_(2))`

Answer

B

Explanation

`vec(r)_(1)=1/(lambda_(1))=R(1/(3^(2))-1/(4^(2))),`
`vec(r)_(2)=1/(lambda_(2)) =R(1/(2^(2))-1/(3^(2)))`
`vec(v)=1/(lambda)=R(1/(2^(2))-1/(4^(2)))`
`:. 1/(lambda)=1/(lambda_(1))+1/(lambda_(2))=(lambda_(1)+lambda_(2))/(lambda_(1)lambda_(2))`
or `lambda=(lambda_(1)lambda_(2))/(lambda_(1)+lambda_(2))`