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 = 1,

m_ℓ = −1

_____ electrons

(b)

n = 4,

ℓ = 3

____ electrons

(c)

n = 4

______ electrons

Answer 1

for each 'n' shell, value of l will be from '0 to n - 1', for each value of l, value of ml will be from '-l to +l', for each ml there will be maximum two electrons.

From this rule, which is known as pauli's exclusion principle:

Part A:

when n = 4, l = 1 ml = -1

there will max 2 electrons.

Part B.

when n = 4 and l = 3,

then ml can be range from -3 to +3, and each ml will contain two electrons so

max electron in this case = 14 electrons

Part C.

when n = 4

there can be 4 different values of l (0, 1, 2, 3), and when

l = 0, then ml = 0, max electron = 2

l = 1, then ml = -1, 0, +1, So max electron = 6

l = 2, then ml = -2, -1, 0, +1, +2, So max electron = 10

l = 3, then ml = -3, -2, -1, 0, +1, +2, +3, So max electron = 14

Now total electrons when n = 4 will be

max electrons = 2 + 6 + 10 + 14 = 32 electrons

Please Upvote.

Comment below if you have any query.