Question

Which of the following electronic transitions are allowed in the hydrogen atom?

a.) 2s --> 1s

b.) 2p--> 1s

c.) 3d-->2p

d.) 3s-->5d

e.) 3s--> 5p

Answer 1

(a) For the hydrogen atom, the selection rule for a transition(whether the transition is allowed or forbidden) are

n = integer, and l = 1.

n and l correspond to the difference in principal quantum numbers and azimuthal quantum numbers. For example - 2s 1s, n = 1-2 = -1(integer) and l corresponding to s-orbital is 0 thus, l = 0 - 0 = 0.

In the above example,  l 1, thus the transition is not allowed.

Similarly in (b), 2p 1s, n = 1-2 = -1 and l = 0 - 1 = -1. This follows the selection rules so the transition is allowed.

In (c), 3d 2p, n = 2 - 3 = -1 and l = 1 - 2 = -1. This follows the selection rules so the transition is allowed.

In (d), 3s 5d, n = 5 - 3 = 2 and l = 2 - 0 = 2. This doesn't follow the selection rules so the transition is forbidden.

In (e), 3s 5p, n = 5 - 3 = 2 and l = 1 - 0 = 1. This follows the selection rules so the transition is allowed.  

Thus (b), (c), and (e) are the allowed electronic transitions.