In: Physics
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
(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.