How many possible sets of electron states (or quantum numbers)are there in the 5f subshell?
A)2
B)8
C)10
D)14

Question

Quizplus · Accepted Answer

The 5f subshell has a total of 7 orbitals, each of which can hold two electrons (one with spin up and one with spin down). Therefore, the total number of possible sets of electron states in the 5f subshell is 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128. However, some of these sets may not be allowed due to the Pauli exclusion principle or Hund's rule. In general, the total number of possible sets of electron states in a subshell is equal to the sum of the possible values of l (the azimuthal quantum number) and s (the spin quantum number), which for the 5f subshell are l = 3, 2, 1, 0 and s = +1/2, -1/2. Therefore, the total number of possible sets of electron states in the 5f subshell is 3 + 2 + 1 + 0 = 6 for each value of s, giving a total of 2 x 6 = 12 possible sets. However, some of these sets may be degenerate (i.e. have the same energy), so we need to add the number of degeneracies, which is 2 for each set (one for spin up and one for spin down). Therefore, the total number of possible sets of electron states in the 5f subshell is 12 x 2 = 24. However, we need to exclude sets that violate the Pauli exclusion principle or Hund's rule, which leaves us with a total of 14 possible sets.

How Many Possible Sets of Electron States (Or Quantum Numbers)are