What is the maximum number of electrons in an atom that can have the following quantum numbers? part an=2 ms= -1/ bn=5, l= cn=4, l=3, ml= - dn=4, l=1, ml=

(A) n=2 and ms = (-1/2) ⇒ 4 electrons.

(B) n = 5 and ℓ = 3 ⇒ 14 electrons

(C) n=4, ℓ=3, mℓ= -3 ⇒  2 electrons

(D) n = 4, ℓ =1, mℓ =1 ⇒  2 electrons

Explanation:

Quantum numbers are the set of numbers that describe the state of an electron in an atom. There are four quantum numbers:

Principal: n ≥ 1

Azimuthal: ℓ ≤ (n-1)

Magnetic: mℓ = (-ℓ) to (ℓ)

Spin: ms = (±1/2)

(A) For: n = 2

ℓ = 0 ⇒ s-orbital and ℓ = 1 ⇒ p-orbital

So, ℓ =0, mℓ = 0 ⇒ 1 orbital

So for, ℓ = 1 , mℓ = -1, 0, +1 ⇒ 3 orbitals

Since an orbital can't have more than two electrons.

Therefore, the maximum number of electrons having n = 2 is 4 × 2 = 8 electrons

As electrons in an orbit must have opposite spins.

Therefore, the total number of electrons having, n=2 and ms = (-1/2) is 8÷2 = 4 electrons.

(B) For: n = 5

ℓ = 0, 1, 2, 3, 4

Now ℓ = 3 ⇒ f-orbital

So for, ℓ = 3,  mℓ = -3 -2, -1, 0, +1, +2, +3 ⇒ 7 orbitals

Since an orbital can't have more than two electrons.

Therefore, the maximum number of electrons having n = 5 and ℓ = 3 is 7 × 2 = 14 electrons

(C) For: n = 4

ℓ = 0, 1, 2, 3

Now ℓ = 3 ⇒ f-orbital

So for, ℓ = 3,  mℓ = -3 -2, -1, 0, +1, +2, +3 ⇒ 7 orbitals

When mℓ= -3 ⇒ 1 orbital

Since an orbital can't have more than two electrons.

Therefore, the maximum number of electrons having n=4, ℓ=3, mℓ= -3 is 1 × 2 = 2 electrons

(D) For: n = 4

ℓ = 0, 1, 2, 3

Now ℓ = 1 ⇒ p-orbital

So for, ℓ = 1 , mℓ = -1, 0, +1 ⇒ 3 orbitals

When mℓ= +1 ⇒ 1 orbital

Since an orbital can't have more than two electrons.

Therefore, the maximum number of electrons having n = 4, ℓ =1, mℓ =1 is 1 × 2 = 2 electrons