Three energy levels of an atom are shown in figure . The wavelength corresponding to three possible transition are `lambda_(1) , lambda_(2)., and lambda_(3)`. The value of `lambda_(3)` in terms of `lambda_(1) and lambda_(2)` is given by

Options

A. `lambda_(1) = lambda_(2) - lambda_(3)`
B. `lambda_(1) = lambda_(3) - lambda_(2)`
C. `(1)/(lambda_(1)) = (1)/(lambda_(2)) + (1)/( lambda_(3))`
D. `(1)/(lambda_(1)) = (1)/(lambda_(3)) + (1)/( lambda_(2))`

Answer

C

Explanation

Let the three energy levels be `E_(1), E_(2), and E_(3)`. The wavelength `lambda_(1), lambda_(2), and lambda_(3)` of the spectral lines corresponding to the three energy transition are depicted as shown in figure.

`E = h f = (h)/(lambda) or E prop (1)/(lambda)`
Thus, for the three wavelength , we have
`{(E_(3) - E_(2) = (h)/(lambda_(3)) ...(i)) , (E_(2) - E_(1) = (h)/(lambda_(2)) ...(ii)) , (E_(3) - E_(1) = (h)/(lambda_(1)) ...(iii)):}`
Now, `E_(3) - E_(1) = (E_(3) - E_(2)) + (E_(2) - E_(1))`
`implies (h)/(lambda_(1)) = (h)/(lambda_(3)) + (h)/(lambda_(2)) implies (1)/(lambda_(1)) = (1)/(lambda_(2)) + (1)/(lambda_(3))`