原子结构

Everything is made of atoms 原子. An atom is mostly empty space. At its centre is a tiny, heavy nucleus 原子核. The nucleus holds two kinds of particle: protons 质子 and neutrons 中子. Around the nucleus, in the empty space, move the electrons 电子. The electrons stay in shells 壳层 — layers at set distances from the nucleus.

The nucleus is very small but holds almost all the mass. The electrons take up almost all the space but have almost no mass.

Relative charge and relative mass

We compare the three particles using relative charge 相对电荷 and relative mass 相对质量. These are simple numbers, not real units.

A proton and a neutron have almost the same mass. An electron is about 1836 times lighter. The proton is positive, the electron is negative, and the neutron has no charge — it is neutral 中性.

Proton number and nucleon number

Two numbers describe the nucleus:

• the proton number 质子数 (also called the atomic number 原子序数), symbol $Z$ — the number of protons.
• the nucleon number 核子数 (also called the mass number 质量数), symbol $A$ — the total number of protons and neutrons. Protons and neutrons are both nucleons 核子.

So the number of neutrons is $A - Z$.

Counting particles in an atom or ion

For a neutral atom, the number of electrons equals the number of protons, which equals $Z$.

An ion 离子 is an atom that has lost or gained electrons, so it has a charge:

• a positive ion has fewer electrons than protons.
• a negative ion has more electrons than protons.

Example: $^{27}_{13}\text{Al}^{3+}$ has $13$ protons, $27 - 13 = 14$ neutrons, and $13 - 3 = 10$ electrons (it lost 3 electrons to become $3+$).

How mass and charge are spread out

Almost all the mass sits in the nucleus, because protons and neutrons are heavy and electrons are very light. All the positive charge is in the nucleus (the protons). The negative charge is spread out in the shells (the electrons).

Beams of particles in an electric field

Imagine beams of protons, neutrons and electrons moving at the same speed into an electric field 电场 between two charged plates:

• the proton beam bends towards the negative plate (protons are positive).
• the electron beam bends the other way, towards the positive plate. It bends much more, because the electron is far lighter — the same force gives a bigger deflection 偏转 to a smaller mass.
• the neutron beam goes straight through. It has no charge, so the field gives it no force.

Atomic radius and ionic radius

The atomic radius 原子半径 is the size of an atom. The ionic radius 离子半径 is the size of an ion.

Across a period 周期 (left to right), the atomic radius gets smaller. The nuclear charge 核电荷 (the pull from the protons) rises, but the electrons go into the same outer shell, so the shielding 屏蔽 by inner shells stays about the same. The stronger pull draws the outer shell inwards.

Down a group 族 (top to bottom), the atomic radius gets larger. Each step down adds a new shell, so the outer electrons are further out and feel more shielding from the nucleus.

For ions:

• a positive ion (cation 阳离子) is smaller than its atom. Electron loss reduces electron-electron repulsion and increases the attraction for the remaining electrons. The whole outer occupied shell may be lost, but not every electron loss empties a shell.
• a negative ion (anion 阴离子) is larger than its atom. It has gained electrons, so there is more repulsion 排斥 between the electrons.
• among ions that have the same number of electrons, the one with more protons is smaller.

Isotopes 同位素 are atoms of the same element with the same number of protons but a different number of neutrons. So isotopes have the same proton number $Z$ but a different nucleon number $A$.

We write an isotope as $^{A}_{Z}\text{X}$: the nucleon number $A$ on top, the proton number $Z$ below. For example, chlorine has two main isotopes, $^{35}_{17}\text{Cl}$ and $^{37}_{17}\text{Cl}$.

Same chemical properties

Chemical properties 化学性质 depend on the electrons, especially the outer electrons. Isotopes of one element have the same number of electrons arranged in the same way. So they react in exactly the same way — they have the same chemical properties.

Different physical properties

Some physical properties 物理性质 depend on mass, so they differ between isotopes. A heavier isotope has more neutrons, so more mass, and therefore a higher density 密度. (The syllabus limits this difference to mass and density.)

Electrons are arranged in shells, sub-shells and orbitals.

Shells and the principal quantum number

Each shell is labelled by the principal quantum number 主量子数 $n = 1, 2, 3, \dots$ A larger $n$ generally means greater spatial extent, but $n$ alone does not put all sub-shells of a multi-electron atom into energy order. The configurations and ionisation processes assessed in these sections are ground-state species from hydrogen to krypton.

Sub-shells and orbitals

Each shell is split into sub-shells 亚层, named s, p and d. Each sub-shell is built from orbitals 轨道. An orbital is a small region that can hold up to two electrons.

So an s sub-shell holds 2 electrons, a p sub-shell holds 6, and a d sub-shell holds 10.

Order of increasing energy

Electrons occupy the lowest-energy available arrangement. The usual neutral-atom filling sequence for the sub-shells studied here is:

4s is reached before 3d in this usual construction sequence. The ordering is not fixed in every occupied atom or ion; apply the separate 4s-first removal rule for transition-metal cations.

Electronic configuration

The electronic configuration 电子排布 lists how many electrons are in each sub-shell. The lowest-energy arrangement is the ground state 基态.

For iron (Fe, $Z = 26$):

You can write a shorthand using the nearest noble gas 稀有气体 in square brackets:

Here $[\text{Ar}]$ stands for the full configuration of argon. Chromium and copper are exceptions to mechanically placing two electrons in 4s: Cr is $[\text{Ar}]3\text{d}^5 4\text{s}^1$ and Cu is $[\text{Ar}]3\text{d}^{10}4\text{s}^1$. Both totals and ground-state occupations matter.

For ions, you add or remove electrons. One key rule: when a transition metal forms a positive ion, it loses its 4s electrons before its 3d electrons. So $\text{Fe}^{3+}$ is $[\text{Ar}]\,3\text{d}^5$.

Electrons in boxes

The electrons in boxes notation draws each orbital as a box and each electron as an arrow. Two electrons in the same orbital must point opposite ways, because each electron has a property called spin 自旋, and a shared orbital needs opposite spins.

Within a sub-shell, electrons fill empty orbitals one at a time, with parallel arrows, before any orbital gets a second electron. Spreading out like this keeps the electrons apart and lowers the repulsion between them.

For oxygen, 2p⁴ has one pair and two singly occupied orbitals. The n = 2 shell also contains the 2s pair, so it contains two pairs altogether. A whole-shell question and a named-sub-shell question have different counting boundaries.

Why the configuration takes this shape

Electrons fill from low energy to high energy because that gives the most stable (lowest-energy) atom. Within a sub-shell they spread out singly first to reduce the repulsion between the negative electrons.

Shapes of s and p orbitals

• an s orbital is a sphere 球形 centred on the nucleus.
• a p orbital has two lobes, like a dumbbell, pointing along one axis. The three p orbitals point along three directions at right angles (the $x$, $y$ and $z$ axes).

Free radicals

A free radical 自由基 is a species with one or more unpaired electrons 未成对电子. Many free radicals are reactive, but the defining feature is an unpaired electron, not reactivity alone or a net charge.

First ionisation energy

The first ionisation energy 第一电离能 (IE) is the energy needed to remove one electron from each atom in one mole of gaseous atoms, forming one mole of gaseous $+1$ ions.

Starting from separate gaseous atoms isolates electron removal without adding energy for breaking a solid or molecule into atoms. The unit is $\text{kJ mol}^{-1}$. As an equation, for an element X:

The $(\text{g})$ shows the species is a gas.

Successive ionisation energies

After removing one electron, you can remove another. The second ionisation energy removes one electron from each $+1$ ion:

You can keep going. These are the successive ionisation energies 逐级电离能. Each is larger than the one before, because every electron is pulled away from a more positive ion.

What ionisation energy depends on

Ionisation energy comes from the attraction between the positive nucleus and the outer electron. Three main factors set how strong that attraction is:

• nuclear charge: more protons pull the electrons more strongly, so the ionisation energy is higher.
• atomic radius: the further the outer electron sits from the nucleus, the weaker the pull, so the ionisation energy is lower.
• shielding: inner shells block some of the pull on the outer electron. More inner shells mean more shielding and a lower ionisation energy.

There is a smaller effect too — spin-pair repulsion 自旋成对排斥. When two electrons share one orbital, they push each other a little, so one is easier to remove.

Trends in first ionisation energy

Across a period, the first ionisation energy generally rises. The nuclear charge grows while shielding stays about the same, so the outer electrons are held more tightly.

Down a group, the first ionisation energy falls. Lower elements have more shells, so more shielding and a larger radius, and the outer electron is easier to remove.

The dips are evidence for sub-shells

The rise across a period is not smooth. Two small dips appear, and you should be able to explain both:

• Group 2 to Group 13 (for example Mg to Al): the electron removed from Al comes from a 3p sub-shell, which is higher in energy than the full 3s sub-shell in Mg. A 3p electron is easier to remove, so the value dips.
• Group 15 to Group 16 (for example P to S): in S, one 3p orbital now holds a pair of electrons. Spin-pair repulsion makes one of them easier to remove, so the value dips.

These dips are evidence that sub-shells exist.

Successive ionisation energies are evidence for shells

If you plot the successive ionisation energies of one element, the values rise, with big jumps at certain points. A big jump happens when the next electron must come from a shell closer to the nucleus.

For main-group atoms, count the electrons removed before the first inner-shell jump to find the outer-shell count. Counts 1 and 2 correspond to Groups 1 and 2; counts 3–8 correspond to Groups 13–18, with helium as the two-electron Group 18 exception. The first jump alone does not establish the period: use the number of occupied shells from fuller data or additional information about the atom.

Worked example. The first five successive ionisation energies of an element are $590$, $1150$, $4940$, $6480$ and $8120\ \text{kJ}\,\text{mol}^{-1}$. Which group is it in? Look for the big jump, not the biggest number. From the 1st to the 2nd the value roughly doubles, which is a normal rise. From the 2nd ($1150$) to the 3rd ($4940$) it more than quadruples: that is the jump. So two electrons come off easily before it, the outer shell holds 2 electrons, and the element is in Group 2. Count the electrons removed before the jump, and explain the jump properly: the next electron is being pulled from a shell closer to the nucleus, not from a different element.

Common mistakes.

• Leaving out the state symbols in an ionisation-energy equation. The atoms and ions are gaseous: $\text{Na(g)} \rightarrow \text{Na}^+\text{(g)} + \text{e}^-$.
• Writing the equation as $\text{X(g)} + \text{e}^- \rightarrow \text{X}^-\text{(g)}$. That is electron gain; ionisation removes an electron.
• Removing 3d electrons before 4s when a transition metal forms an ion. The 4s electrons go first: $\text{Fe}^{2+}$ is $[\text{Ar}]\,3\text{d}^6$, not $[\text{Ar}]\,3\text{d}^4\,4\text{s}^2$.
• Writing chromium as $[\text{Ar}]\,3\text{d}^4\,4\text{s}^2$ or copper as $[\text{Ar}]\,3\text{d}^9\,4\text{s}^2$. Both are exceptions: Cr is $3\text{d}^5\,4\text{s}^1$ and Cu is $3\text{d}^{10}\,4\text{s}^1$.
• Explaining the Mg → Al dip by spin-pair repulsion. The Al electron is removed from a 3p sub-shell, higher in energy than Mg's 3s; spin-pair repulsion explains the P → S dip.
• Saying successive ionisation energies rise "because there are fewer electrons". Each electron is removed from an increasingly positive ion, so it is held more strongly; a big jump shows a new, inner shell.
• Saying the electron beam bends towards the negative plate. Electrons are negative, so they bend towards the positive plate, and more sharply than protons because their mass is far smaller.

• Define isotopes in full: atoms of the same element with the same number of protons but a different number of neutrons — the mark scheme wants both halves.
• 4s fills before 3d, but electrons are removed from 4s first when forming ions, so $\text{Fe}^{3+}$ is $[\text{Ar}]3\text{d}^5$ (not $[\text{Ar}]3\text{d}^3 4\text{s}^2$).
• In successive ionisation energies, a big jump marks the start of a new (inner) shell — use the jumps to place the element in its group.
• Explain every ionisation-energy trend with the same three factors: nuclear charge, distance and shielding, plus sub-shell effects for the small dips.
• Learn the exact reason first ionisation energy of oxygen is below nitrogen: oxygen's paired 2p electrons repel, so one is easier to remove.