Electronic StructureMedium

Quantum numbers and orbitals

Determine the number of orbitals in subshells and the electron capacity of energy levels.

Given data

rule: orbitals = 2l+1rule: electrons per level = 2n²

Steps

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How many orbitals in the 3d subshell? (l=2)
Write your working — the numerical result must appear in the text
How many orbitals in the 4f subshell? (l=3)
How many electrons can level n=3 hold?

Full worked solution

How many orbitals in the 3d subshell? (l=2)
$2l+1 = 2\cdot2+1$
$2l+1 = 2 \cdot 2 + 1 = 4 + 1 = \mathbf{5}$ . There are 5 orbitals in the 3d subshell.
How many orbitals in the 4f subshell? (l=3)
$2\cdot3+1$
$2l+1 = 2 \cdot 3 + 1 = 6 + 1 = \mathbf{7}$ . There are 7 orbitals in the 4f subshell.
How many electrons can level n=3 hold?
$2n^2 = 2\cdot3^2$
$2n^2 = 2 \cdot 3^2 = 2 \cdot 9 = \mathbf{18}$ . Level n=3 can hold a maximum of 18 electrons.

Result:3d: 5 orbitals — 4f: 7 orbitals — n=3: 18 electrons.

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