The following diagram indicates the energy levels of a certain atom when the system moves from `4E` level to `E`. A photon of wavelength `lambda_(1)` is emitted. The wavelength of photon produced during its transition from `(7)/(3)E` level to `E` is `lambda_(2)`. the ratio `(lambda_(1))/(lambda_(2))` will be

Options

A. `(4)/(9)`
B. `(4)/(8)`
C. `(3)/(8)`
D. `(5)/(9)`

Answer

A

Explanation

For transition from 4E to E
`" " (4E-E)=(hc)/(lambda_(1))rArrlamba_(1)=(hc)/(3E)" "....(i)`
For transition from `(7)/(3)` E to E
`" " ((7)/(3)E-E)=(hc)/(lambda_(2))rArrlambda_(2)=(hc)/(3E)" " ...(ii)`
From Eqs. (i) and (ii) we get , `(lambda_(1))/(lambda_(2))=(4)/(9)`