electron configurations of atoms up to atomic number 36 using the Schrödinger model (shells, subshells, orbitals; spdf notation), and the explanation of trends in the periodic table including atomic radius, first ionisation energy and electronegativity in terms of core charge, shielding and shell number

What this dot point is asking

VCAA wants you to write electron configurations of atoms and ions up to Z = 36 using the Schrödinger model (shells, subshells, orbitals) with spdf notation, and to explain periodic trends (atomic radius, first ionisation energy, electronegativity) in terms of core charge, shielding and shell number.

The answer

Shells, subshells, orbitals

The Schrödinger model places electrons in regions called orbitals, grouped into subshells, grouped into shells.

• Shell (principal quantum number n = 1, 2, 3, ...): roughly an energy level / distance from the nucleus.
• Subshell (s, p, d, f): grouped orbitals of the same shape within a shell.
• Orbital: a 3D region with up to 2 electrons (opposite spins).

Subshell capacities:

Filling order (aufbau)

Subshells fill from lowest energy upward. For neutral atoms up to Z = 36 the order is:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p

The 4s subshell fills before the 3d (because, when both are empty, 4s sits slightly lower in energy). Once 3d begins filling, the 4s rises slightly above 3d, which is why transition-metal cations lose 4s electrons before 3d.

spdf notation

Write the subshells in order with the number of electrons as a superscript. The exponents must sum to the total number of electrons. Examples up to Z = 36:

• Carbon (Z = 6): 1s^2 2s^2 2p^2
• Sodium (Z = 11): 1s^2 2s^2 2p^6 3s^1
• Argon (Z = 18): 1s^2 2s^2 2p^6 3s^2 3p^6
• Calcium (Z = 20): 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2
• Iron (Z = 26): 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6
• Bromine (Z = 35): 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^5

Two anomalies you need to know: Cr is [Ar] 4s^1 3d^5 and Cu is [Ar] 4s^1 3d^10 (a half-filled or fully-filled 3d is slightly more stable than a paired 4s).

Ions

For anions, add electrons to the next available orbital. O (1s^2 2s^2 2p^4) gains two electrons to become O^2- (1s^2 2s^2 2p^6).

For cations, remove electrons from the highest-n shell first. For transition metals, that means removing 4s electrons before 3d:

• Fe (4s^2 3d^6) becomes Fe^2+ (3d^6) and Fe^3+ (3d^5).
• Cu (4s^1 3d^10) becomes Cu^+ (3d^10) and Cu^2+ (3d^9).

Periodic trends

Three factors explain almost every trend:

1. Core charge (effective nuclear charge): the net positive charge felt by a valence electron after accounting for inner-shell shielding. Roughly equal to the group number for main-group elements.
2. Shielding: electrons in inner shells reduce the pull of the nucleus on the valence electrons.
3. Shell number (n): a larger n means valence electrons sit further from the nucleus.

Atomic radius

• Across a period (left to right): core charge increases, shielding is roughly constant, shell number is constant. Valence electrons are pulled closer. Radius decreases.
• Down a group: shell number increases (added shells), shielding increases. Valence electrons sit further out. Radius increases.

First ionisation energy

The energy to remove the most loosely held electron from a gaseous atom.

• Across a period: stronger pull on valence electrons (higher core charge, same n) means ionisation energy increases.
• Down a group: weaker pull on valence electrons (higher n, more shielding) means ionisation energy decreases.

Small dips exist within a period (Mg to Al, P to S) due to subshell effects, but the overall trend is upward.

Electronegativity

The tendency of an atom to attract a shared pair of electrons in a covalent bond.

• Across a period: electronegativity increases for the same reason as ionisation energy.
• Down a group: electronegativity decreases.

Fluorine sits in the top right (excluding noble gases) and is the most electronegative element on the Pauling scale (4.0). Caesium and francium are the least electronegative.

Worked example

Compare the first ionisation energies of Na, Mg, Al and write configurations.

Configurations:

• Na (Z = 11): 1s^2 2s^2 2p^6 3s^1
• Mg (Z = 12): 1s^2 2s^2 2p^6 3s^2
• Al (Z = 13): 1s^2 2s^2 2p^6 3s^2 3p^1

Predicted order Na < Mg < Al (core charge rising left to right). Actual order Na < Al < Mg.

The dip from Mg to Al happens because Al's outermost electron is in the 3p subshell, slightly higher in energy and more shielded by the filled 3s^2 below it, so it is easier to remove than Mg's 3s^2 electron.

Common traps

Writing 3d before 4s in a neutral atom. Filling order for neutral atoms is 4s before 3d. (Order in cations is the reverse.)

Removing 3d electrons first when ionising a transition metal. Always remove the 4s electrons first.

Forgetting Cr and Cu are anomalies. Both promote one 4s electron into 3d for extra stability.

Saying nuclear charge instead of core charge. Nuclear charge is the full +Z. Core charge is what's left after the inner shells shield it. Use the latter when explaining periodic trends.

Mixing radius and ionisation energy trends. They go in opposite directions (radius and ionisation energy are inversely related across both periods and groups).

In one sentence

Electrons occupy shells, subshells and orbitals in the Schrödinger model, the configuration is written in spdf notation with 4s filling before 3d for neutral atoms but emptying first for transition-metal cations, and atomic radius, ionisation energy and electronegativity trends across the periodic table follow directly from how core charge, shielding and shell number change.