Question

Apply the Pauli exclusion principle to determine the number of electrons that could occupy the quantum states described by the following.

a) n = 4, ℓ = 3, mℓ = −2

b) n = 4, ℓ = 2

c) n = 4

Answer 1

(a)

Each has two possible states corresponding to spin up and spin down electron. has two states, one electron with spin up and the other electron with spin down. Therefore, there are 2 states available in , or maximum 2 electrons can occupy this state.

(b)

Each state have possible electronic configurations. Here are the possible configurations, and it is multiplied by two because there are two spin configurations for each value.

For possible m values are:

And each of these m values allow two possible spin configurations of electrons. Therefore, has 10 possiblities of electronic configurations, 10 electrons can occupy this state.

(c)

Each n state has possible electronic configurations. In this all the and spin states are included.

For n=4 there are possible electronic configurations. Therefore, maximum of 32 electrons can occupy n=4 state.