In: Chemistry
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
(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.