The diagram shows the energy levels for an electron in a certain atom.

Which transition shown in the diagram represents the emission of a photon with the maximum energy?

Options

A. IV
B. III
C. II
D. I

Answer

B

Explanation

Transition I shows absorption of photons . For (II) ,` n_i = 4 "and " n_f = 3`
`therefore` energy of the emitted photon is given by
`therefore Delta E_1 = K [(1)/(n_f^2 ) - (1)/(n_i^2)] = K [ (1)/(3^2) - (1)/(4^2) ] = 7/144 K`
For (III), `n_i =2 " and " n_f = 1`
`therefore DeltaE_2 =K [ (1)/(1^2) - (1)/(2^2)] = 3/4 K`
For (IV), `n_i = 4 " and " n_f = 2`
`therefore DeltaE_3 = K [ (1)/(2^2) - (1)/(4^2) ] = K [1/4 - 1/16] = 3/16 K`
Thus `DeltaE_2` is maximum for the transition III.