Atomic Structure: Question 9

Worked solution

Part (a): Maximum electrons per orbital

A single atomic orbital can hold a maximum of 2 electrons. Electrons are negatively charged and repel one another, but if the two electrons in an orbital have opposite (paired) spins, this partly offsets the repulsion enough for both to occupy the same orbital. A third electron would necessarily have the same spin as one of the existing pair, which is not permitted in the same orbital. This is why 2 is the maximum.

Part (b): Orbitals and capacity of each sub-shell

Part (c): Maximum capacity of the third shell

The third shell ($n=3$) is made up of the $3s$, $3p$ and $3d$ sub-shells. Using the maximum capacities from part (b):

$2 \ (3s) + 6 \ (3p) + 10 \ (3d) = 18$

So the third shell can hold a maximum of $18$ electrons.

Part (d): Electron arrangement in oxygen’s 2p sub-shell

Oxygen (proton number 8) has the configuration $1s^2\,2s^2\,2p^4$, so 4 electrons occupy the three $2p$ orbitals. Following Hund’s rule, each of the three orbitals is first occupied singly (with parallel spins) before any pairing occurs, this accounts for the first 3 electrons, one per orbital. The fourth electron cannot start a new orbital (there are only three $2p$ orbitals), so it must pair up with one of the existing electrons, occupying the same orbital with the opposite spin.

The final arrangement is: one orbital with a pair of electrons (opposite spins), and two orbitals each with a single unpaired electron. Oxygen therefore has $\boxed{2}$ unpaired electrons overall (the pair in the third $2p$ orbital does not count as unpaired).

Final answers

• (a) $\boxed{2}$ electrons per orbital, with opposite (paired) spins.
• (b) $s$: 1 orbital / 2 electrons. $p$: 3 orbitals / 6 electrons. $d$: 5 orbitals / 10 electrons.
• (c) $2+6+10 = \boxed{18}$ electrons maximum in the third shell.
• (d) One $2p$ orbital paired, two singly occupied $\Rightarrow$ $\boxed{2}$ unpaired electrons.