Cambridge International A-Level Chemistry

Particles in the atom

An atom is mostly empty space. Nearly all of its mass sits in a very small, dense nucleus made of protons and neutrons, and the electrons occupy shells in the space around it. The nucleus carries all of the positive charge and almost all of the mass, while the electrons carry all of the negative charge and almost none of the mass.

The proton number (atomic number, $Z$) is the number of protons in the nucleus, and it decides which element an atom is. The nucleon number (mass number, $A$) is the total number of protons and neutrons. In an atom the number of electrons equals the number of protons, so the atom is neutral; an ion has gained or lost electrons.

For a species written as $\ce{^{A}_{Z}X^{n+}}$ or $\ce{^{A}_{Z}X^{n-}}$:

• protons $= Z$
• neutrons $= A - Z$
• electrons $= Z - n$ for a cation of charge $n+$, and $Z + n$ for an anion of charge $n-$

For example, $\ce{^{27}_{13}Al^{3+}}$ has 13 protons, 14 neutrons and 10 electrons, while $\ce{^{32}_{16}S^{2-}}$ has 16 protons, 16 neutrons and 18 electrons.

Beams in an electric field

Suppose a beam of each particle, all travelling at one speed, is sent between two charged plates. The three beams behave differently. Protons are attracted towards the negative plate and electrons towards the positive plate. Neutrons have no charge and pass straight through undeflected. The electron beam bends further than the proton beam, because the electron has the same size of charge as the proton but a mass around 1800 times smaller, so the same force gives it a much larger acceleration.

Atomic and ionic radius

Across a period the nuclear charge increases while electrons are added to the same shell, so there is no extra shielding. The outer electrons are pulled in more strongly and the atomic radius falls. Down a group each element has an extra shell, the outer electrons are further from the nucleus and are shielded by more inner shells, so the radius increases.

Ionic radii follow the same trends within a group. A cation is smaller than its atom because the outer shell has been lost and the remaining electrons are pulled in by the same nuclear charge; an anion is larger than its atom because the added electrons repel one another while the nuclear charge is unchanged. Across a period of isoelectronic ions (for example $\ce{Na+}$, $\ce{Mg^{2+}}$, $\ce{Al^{3+}}$, all with 10 electrons) the radius falls as the nuclear charge rises. The anions $\ce{N^{3-}}$, $\ce{O^{2-}}$ and $\ce{F-}$ are larger than the cations because their outer electrons are in the second shell, while the cations have lost the third shell.

Isotopes

Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. Chlorine has $\ce{^{35}Cl}$ with 18 neutrons and $\ce{^{37}Cl}$ with 20 neutrons, and carbon has $\ce{^{12}C}$, $\ce{^{13}C}$ and $\ce{^{14}C}$ with 6, 7 and 8 neutrons.

Isotopes of one element have the same chemical properties because chemical behaviour is decided by the number and arrangement of electrons, which is set by the proton number. They have different physical properties, in particular mass and density, because the number of neutrons changes the mass of the atom. The heavier isotope also diffuses more slowly, since its atoms move more slowly at the same temperature.

Shells, sub-shells and orbitals

Electrons occupy shells numbered by the principal quantum number, $n = 1, 2, 3, 4$. Each shell contains one or more sub-shells (s, p, d), and each sub-shell is made of orbitals. An orbital is a region of space around the nucleus that can hold up to two electrons, which must have opposite spins.

The first shell holds only an s sub-shell, the second holds s and p, and the third and fourth hold s, p and d (the 4f sub-shell is not needed). A shell $n$ can hold up to $2n^2$ electrons, so 2, 8, 18 and 32.

An s orbital is spherical, and its size increases with $n$. A p sub-shell consists of three dumb-bell shaped orbitals, each with two lobes, pointing along the $x$, $y$ and $z$ axes at right angles to one another.

Order of filling

In the ground state, electrons occupy the lowest-energy orbitals available. The order of increasing energy of the sub-shells is:

The 4s sub-shell is filled before 3d because, for the first transition series, it is lower in energy when the 3d sub-shell is empty. Two rules decide how electrons go into a sub-shell with more than one orbital. Electrons go into separate orbitals of the same energy with parallel spins before any orbital holds a pair, because two electrons in one orbital repel each other and a half-filled arrangement has lower energy. Two electrons in one orbital must have opposite spins.

Writing configurations

Two conventions are used. Iron, with 26 electrons, is $1\text{s}^2 2\text{s}^2 2\text{p}^6 3\text{s}^2 3\text{p}^6 3\text{d}^6 4\text{s}^2$ in full, or $[\text{Ar}]\,3\text{d}^6 4\text{s}^2$ in shorthand, where $[\text{Ar}]$ stands for the argon core. In the electrons-in-boxes notation each orbital is a box and each electron an arrow. For the 3d and 4s sub-shells of iron there is one box for the 4s orbital holding an opposite-spin pair, and five boxes for 3d, with one box holding a pair and four holding single electrons with parallel spins.

Only elements from hydrogen to krypton are needed, and two of them are exceptions to the simple filling order. Chromium is $[\text{Ar}]\,3\text{d}^5 4\text{s}^1$ and copper is $[\text{Ar}]\,3\text{d}^{10} 4\text{s}^1$. In each case promoting one 4s electron gives a half-filled or full 3d sub-shell, and the lower repulsion between electrons more than makes up for the small energy cost.

Ions

When a transition element forms a positive ion, the 4s electrons are lost before the 3d electrons. So $\ce{Fe^{2+}}$ is $[\text{Ar}]\,3\text{d}^6$, $\ce{Fe^{3+}}$ is $[\text{Ar}]\,3\text{d}^5$ and $\ce{Cu^{2+}}$ is $[\text{Ar}]\,3\text{d}^9$. The 3d sub-shell drops below 4s in energy once it starts to fill, which is why the outer 4s electrons are the ones removed. Negative ions are found by adding electrons to the atom's configuration, so $\ce{Cl-}$ is $1\text{s}^2 2\text{s}^2 2\text{p}^6 3\text{s}^2 3\text{p}^6$, the same as argon.

Free radicals

A free radical is a species with one or more unpaired electrons. A chlorine atom, $\ce{Cl.}$, has seven outer electrons with one of them unpaired, and this is why free radicals are so reactive.