Particles in the atom and atomic radius

An atom is built from three particles. You must know their relative charge and relative mass precisely.

Particle	Relative charge	Relative mass	Location
Proton	$+1$	$1$	Nucleus
Neutron	$0$	$1$	Nucleus
Electron	$-1$	$\tfrac{1}{1836}\;(\approx 0.000549)$	Shells (orbitals) around the nucleus

Why the nucleus matters so much.

• The nucleus is tiny but holds the protons and neutrons, so it carries nearly 100% of the atomic mass and all of the positive charge.
• Electrons have negligible mass (about $\tfrac{1}{1836}$ of a proton), so they barely contribute to mass — but they occupy essentially all of the volume of the atom.
• An atom is therefore mostly empty space: if the nucleus were the size of a pea, the atom would be the size of a sports stadium.

Neutral atom. Number of electrons $=$ number of protons, so the charges cancel.

Key terms.

• Proton number / atomic number, $Z$ = number of protons. It defines the element — change $Z$ and you change the element.
• Nucleon number / mass number, $A$ = number of protons $+$ neutrons (the particles in the nucleus are collectively the nucleons).
• Nuclide notation: $^{A}_{Z}\text{X}$

Counting the particles.

• Protons $= Z$.
• Neutrons $= A - Z$.
• Electrons $= Z - (\text{charge})$. For a neutral atom, electrons $= Z$.

Worked — neutral atom. $^{27}_{13}\text{Al}$: protons $= 13$, neutrons $= 27 - 13 = 14$, electrons $= 13$.

Worked — a cation. $^{24}_{12}\text{Mg}^{2+}$: protons $= 12$, neutrons $= 24 - 12 = 12$, electrons $= 12 - 2 = 10$ (lost 2 electrons to become $2+$).

Worked — an anion. $^{16}_{8}\text{O}^{2-}$: protons $= 8$, neutrons $= 8$, electrons $= 8 - (-2) = 10$ (gained 2 electrons to become $2-$).

A favourite exam scenario: beams of protons, neutrons and electrons, all moving at the same velocity, pass between two oppositely charged plates.

What controls the deflection?

• The electric force on a charged particle is $F = qE$.
• The resulting deflection (sideways acceleration) is proportional to $\dfrac{\text{charge}}{\text{mass}}$.

Conclusions to state in the exam:

• Neutron — no charge, so no force → travels straight through, undeflected.
• Proton — positive, so it is attracted towards the negative plate.
• Electron — negative, so it is attracted towards the positive plate — the opposite direction to the proton.
• The electron is deflected much more than the proton (by a factor of about $1836$) because it has the same magnitude of charge but a far smaller mass, giving a much larger charge/mass ratio.

Atomic radius across a period (left → right). Decreases.

• Each step adds one proton (nuclear charge $+1$) and one electron to the same outer shell.
• Shielding by inner shells stays roughly constant, so the effective nuclear charge increases.
• The stronger pull draws the outer shell closer → smaller atom. (e.g. Na > Mg > Al > … > Cl.)

Atomic radius down a group. Increases.

• Each step adds a new outer shell, so the outer electrons are in a higher principal quantum level, further from the nucleus.
• More inner shells means more shielding, which offsets the larger nuclear charge.
• Net effect: outer electrons are held less tightly and sit further out → larger atom. (e.g. Li < Na < K.)

Ionic radius.

• Cations are smaller than their parent atom. Losing electrons often removes the entire outer shell, and the remaining electrons feel a greater nuclear charge each, so they are pulled in. (Na $0.186\,\text{nm}$ → Na$^+$ $0.095\,\text{nm}$.)
• Anions are larger than their parent atom. Adding electrons increases electron–electron repulsion while the nuclear charge is unchanged, so the electron cloud expands. (Cl $0.099\,\text{nm}$ → Cl$^-$ $0.181\,\text{nm}$.)

Isoelectronic species (same number of electrons): radius decreases as nuclear charge increases, because the same number of electrons is pulled in more strongly. $\text{N}^{3-} > \text{O}^{2-} > \text{F}^- > \text{Na}^+ > \text{Mg}^{2+} > \text{Al}^{3+}$ (All have 10 electrons; the radius falls as $Z$ rises from 7 to 13.)