The rubidium atom has 37 electrons and its electron configuration is, Rb: 1s22s22p63s23p64s23d104p64d105s1, which means that there is a valence electron in the 5s orbital. The fact that rubidium's only valence electron is in the 5s orbital tells us something about it's quantum numbers. The quantum numbers for the rubidium atom are as follows:
The quantum number n = 5 corresponds to the O shell, and l = 0 tells us that the valence electron is in an s orbital. The magnitude of the spin angular momentum, s, is equal to 1/2 for any electron. The z component of the spin angular momentum, ms , is equal to positive or negative 1/2 for any electron. The magnitude of the total angular momentum, J, is determined by the formula, |L-S| < J < L+S, and it changes in steps of one. From this formula, we can calculate j for rubidium to be +1/2. We can now use the term 5s1/2 to describe the energy level of the valence electron for the rubidium atom, where the subscript "1/2" is the value of j.
The valence electron in the 5s orbital can be excited to the 5p orbital. If this transition takes place, the quantum numbers describing the rubidium atom change. The new quantum numbers for the excited rubidium atom are:
As before, n = 5 indicates that the valence electron is still in the O shell. Now, however, l = 1 which means that the electron now resides in a p orbital. The magnitude of the spin angular momentum and its z component remain unchanged. The value of j changes with a change in the value of l. The total angular momentum is now equal to 1/2 or 3/2. The value of the total angular momentum is quantized meaning that j can only equal two discrete values, 1/2 and 3/2.
In the ground state, the energy level for the valence electron of the rubidium atom consisted of a single level, the 5s1/2 . In the excited state, there are two possible values for the total angular momentum, j = 1/2 and j = 3/2. The two possible values for the total angular momentum give rise to a splitting of the 5p orbital. The 5p orbital splits into the 5p1/2 and 5p3/2 levels. The 5p3/2 orbital is at a higher energy level than the 5p1/2 orbital. The resulting energy level diagram is as follows:
This splitting is known as the fine structure of rubidium.
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