Answer:
(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
Step-by-step 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