The nuclear atom: particles, proton and nucleon numbers

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Atoms are mostly empty space surrounding a very small, dense nucleus that contains protons and neutrons; electrons are found in shells (energy levels) in the empty space around the nucleus.

The scale is hard to picture.

A typical atom is about $10^{-10}$ m across, but its nucleus is only about $10^{-15}$ to $10^{-14}$ m across.

If the nucleus were the size of a pea, the atom would be the size of a large sports stadium.

Yet the nucleus holds more than 99.9% of the atom's mass, so it is extremely dense.

The evidence: alpha particles and gold foil

In the early 1900s, Geiger and Marsden, working with Ernest Rutherford, fired a beam of alpha particles at a very thin sheet of gold.

Alpha particles are small, fast and positively charged.

Figure 1.1 shows what happened to them, and Table 1.1 shows what each result tells you.

Figure 1.1: alpha particles fired at a column of gold atoms (not to scale). Most pass straight through the atoms, a few passing close to a nucleus are deflected, and a very small number bounce back off a nucleus.

Key to Figure 1.1: ① most alpha particles pass straight through; ② a particle passing close to a nucleus is pushed away and deflected; ③ a particle heading almost straight at a nucleus is turned back; ④ a gold atom, almost all empty space; ⑤ the nucleus (the dot), tiny, positive and massive.

Table 1.1 What the alpha-particle results show

observation

what it shows

almost all particles pass straight through

the atom is mostly empty space

a few are deflected through large angles

the positive charge is concentrated in a very small region, which repels the positive alpha particles

a very small number bounce back

that small region also holds most of the mass, so it is dense enough to turn a fast particle round

Each result needs the nucleus to explain it.

An answer that says only "the atom is mostly empty" explains the first observation, not the deflections.

The three particles

Protons and neutrons are found in the nucleus, and together they are called nucleons.

Electrons are found in the shells around the nucleus.

Masses and charges are given as relative values, compared with the proton.

Table 1.2 The particles in an atom

particle

where it is found

relative mass

relative charge

proton

nucleus

neutron

nucleus

electron

shells around the nucleus

$\frac{1}{1836}$ (about 0.0005)

−1

Two points matter.

The proton and the neutron have almost the same mass.

The electron's mass is tiny, but it is not zero: "negligible" is fine as a description, "no mass" is wrong.

How mass and charge are distributed

Put Table 1.2 together with the size of the nucleus and you have the full picture.

Mass. Nearly all of the mass is in the nucleus, because protons and neutrons are each about 1836 times heavier than an electron. The nucleus occupies a tiny fraction of the volume, so it is very dense.

Positive charge. All of the positive charge is in the nucleus, carried by the protons.

Negative charge. The negative charge is carried by the electrons, spread out through the large volume around the nucleus.

Overall charge. In an atom the number of electrons equals the number of protons, so the charges cancel and the atom is neutral.

Figure 1.2 is the shell model you met at IGCSE, drawn for carbon-12.

It shows where the particles are, but it cannot be drawn to scale: with the nucleus drawn this size, the atom would be hundreds of metres wide.

Figure 1.2: a shell model of a carbon-12 atom (not to scale): a nucleus of 6 protons and 6 neutrons, with 2 electrons in the first shell and 4 in the second.

Key to Figure 1.2: ① the nucleus, holding 6 protons and 6 neutrons; ② first shell, holding 2 electrons; ③ second shell, holding 4 electrons; ④ an electron.

In Section 5 you will see that each shell is split into sub-shells and orbitals.

Proton number and nucleon number

Every atom is described by two whole numbers.

The proton number (atomic number), $Z$ , is the number of protons. It identifies the element: every atom with 26 protons is iron, whatever else is true of it.

The nucleon number (mass number), $A$ , is the number of protons plus the number of neutrons.

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

Both numbers are written on the symbol: the nucleon number at the top left and the proton number at the bottom left, as in $\ce{^{56}_{26}Fe}$ .

Section 4 uses this notation for isotopes.

Counting particles in atoms and ions

An ion forms when an atom gains or loses electrons.

The nucleus does not change, so the numbers of protons and neutrons stay the same.

Only the electron count changes.

quantity

how to find it

protons

$Z$

neutrons

$A - Z$

electrons

$Z$ − charge (so subtract for a positive ion, add for a negative ion)

For a group of atoms, such as a molecule or a polyatomic ion, add up the protons and neutrons of every atom, then adjust the electron total by the charge.

The idea behind it

Why did the gold-foil results need a nucleus at all?

Before 1911 the favoured picture, J. J. Thomson's "plum pudding" model, spread the positive charge thinly through the whole atom, with the electrons dotted through it.

An alpha particle is about 7300 times heavier than an electron, so the electrons could no more turn it round than a few table-tennis balls could stop a bowling ball.

Only the positive charge could do that, and spread thinly it was far too weak.

The electric force between two charges grows as they get closer, but only while you are still outside the charge.

Push into a spread-out ball of charge and much of it is now around you instead of in front of you, so the push gets weaker again.

Now squeeze the same positive charge into a region about ten thousand times smaller across.

An alpha particle can get about ten thousand times closer to it, and the force grows with the square of how much closer you get, so the strongest push is about $10^4 \times 10^4 = 10^8$ times larger.

That is the difference between a gentle nudge and a head-on rebound, and it is why the rare large deflections, not the many straight paths, were the real discovery.

The figure compares the two pictures.

Log-log graph of the strength of the push on an alpha particle against distance from the centre of an atom. If the positive charge is spread through the whole atom (radius about 10⁻¹⁰ m), the push rises as the particle approaches but peaks at the edge of the atom and falls inside it. If the same charge is concentrated in a nucleus about 10⁻¹⁴ m across, the push keeps rising until the edge of the nucleus, reaching about 10⁸ times the largest value for the spread-out charge

It helps to see the nucleus and the electrons as doing two different jobs.

The nucleus supplies the mass and the positive charge, and nothing in chemistry changes it.

The electrons supply the size of the atom and its behaviour: they are what atoms share, transfer and rearrange.

That is why the proton number, not the nucleon number, identifies an element.

$Z$ fixes the charge on the nucleus, which fixes how many electrons a neutral atom holds and how tightly it holds them, and that decides the chemistry.

Counting particles in an ion then needs no rule to remember: the nucleus is untouched, so only the electron count moves.

You may wonder what holds a nucleus together, since its protons are packed very close and all repel one another.

The answer is a different force, the strong nuclear force, which acts between nucleons only over distances about the size of a nucleus; neutrons add to it without adding any repulsion.

That is physics, not chemistry, and it is not examined here.

What matters for you is a consequence of Table 1.2: because protons and neutrons each have a relative mass close to 1 and electrons count for almost nothing, the nucleon number is very nearly the mass of the atom on the relative scale.

Unit 2 builds relative atomic masses on exactly that.

Key terms

Proton (atomic) number: the number of protons in the nucleus of an atom.

Nucleon (mass) number: the total number of protons and neutrons in the nucleus of an atom.

Nucleon: a particle found in the nucleus, either a proton or a neutron.

Nucleus: the very small, dense, positively charged centre of an atom, which contains the protons and neutrons.

Ion: a species with an overall charge, because its number of electrons is different from its number of protons.

Learn these word for word.

The marks hang on "number of protons" and "protons and neutrons", not on "mass" or "weight".

Worked example 1: particles in a positive ion (AO1 · L1)

Determine the numbers of protons, neutrons and electrons in the ion $\ce{^{56}_{26}Fe^3+}$ .

1. Protons $= Z = 26$ .

2. Neutrons $= A - Z = 56 - 26 = 30$ .

3. Electrons: the 3+ charge means three electrons have been lost, so $26 - 3 = 23$ .

Answer: 26 protons, 30 neutrons, 23 electrons.

Worked example 2: completing a table of ions (AO2 · L2)

Complete the table for four ions.

Proton numbers: Al 13, S 16, K 19, Br 35.

ion

protons

neutrons

electrons

$\ce{^{27}Al^3+}$

$27 - 13 = 14$

$13 - 3 = 10$

$\ce{^{32}S^2-}$

$32 - 16 = 16$

$16 + 2 = 18$

$\ce{^{39}K+}$

$39 - 19 = 20$

$19 - 1 = 18$

$\ce{^{81}Br-}$

$81 - 35 = 46$

$35 + 1 = 36$

1. Read $Z$ from the Periodic Table: it fixes the protons.

2. Subtract $Z$ from the nucleon number for the neutrons.

3. Adjust by the charge for the electrons: a 2− ion has gained two, so add 2.

Answer: as in the table.

Notice that $\ce{S^2-}$ and $\ce{K+}$ both have 18 electrons, the same as an argon atom.

Species with the same number of electrons are isoelectronic; Section 3 uses this idea.

Worked example 3: working backwards to the species (AO2 · L3)

(a) A species has 16 protons, 18 neutrons and 18 electrons. Identify it and write its full symbol. (b) Determine the numbers of protons, neutrons and electrons in the ammonium ion made of $\ce{^{14}N}$ and $\ce{^{1}H}$ atoms.

1. (a) 16 protons means sulfur, $Z = 16$ .

2. Nucleon number $= 16 + 18 = 34$ .

3. It has 2 more electrons than protons, so its charge is 2−.

4. (b) $\ce{NH4+}$ has one N and four H. Protons $= 7 + 4 \times 1 = 11$ .

5. Neutrons: $\ce{^{14}N}$ has $14 - 7 = 7$ ; $\ce{^{1}H}$ has none. Total 7.

6. Electrons $= 11 - 1 = 10$ .

Answer: (a) $\ce{^{34}_{16}S^2-}$ ; (b) 11 protons, 7 neutrons, 10 electrons.

Worked example 4: how much of the mass is in the nucleus? (AO2 · L3)

Show that more than 99.9% of the mass of a carbon-12 atom (6 protons, 6 neutrons, 6 electrons) is in its nucleus.

Use the relative masses in Table 1.2.

1. M1: mass of the nucleus $= 6 \times 1 + 6 \times 1 = 12$ .

2. M2: mass of the electrons $= 6 \times \frac{1}{1836} = 0.00327$ .

3. M3: percentage in the nucleus $= \dfrac{12}{12 + 0.00327} \times 100 = 99.97\%$ .

Answer: 99.97% of the mass is in the nucleus, which is more than 99.9%.

Keep the unrounded electron mass in the last step, and round only the final answer.

Exam tip

When asked how mass and charge are distributed in an atom, give four linked points: the mass is concentrated in the nucleus (protons and neutrons), the positive charge is in the nucleus, the negative charge (electrons) is spread in shells around it, and the atom is mostly empty space.

Mention both mass and charge, or the answer is incomplete.

Common mistakes

Wrong: the nucleon number is the number of neutrons, or is the same as the relative atomic mass. Right: the nucleon number is protons plus neutrons, a whole number for one isotope. The relative atomic mass is an average over isotopes (unit 2).

Wrong: a 3+ ion has three extra electrons. Right: a positive charge means electrons were lost, so subtract: $\ce{Fe^3+}$ has $26 - 3 = 23$ .

Wrong: the alpha-particle results are explained by "the atom is empty space" alone. Right: the large deflections need a small, dense, positive nucleus; say so.

Wrong: electrons have no mass. Right: they have a relative mass of about $\frac{1}{1836}$ , small enough to call negligible.

Check your understanding

1. Which row is correct for the ion $\ce{^{71}_{31}Ga^3+}$ ? AO2 · L2 [1]

protons

neutrons

electrons

2. Which statement about an atom of $\ce{^{23}_{11}Na}$ is correct? AO1 · L2 [1]

A Its mass is spread evenly through its volume.
B Its 11 electrons make up about half of its mass.
C Almost all of its mass and all of its positive charge are in a nucleus that fills a tiny fraction of its volume.
D Its 12 neutrons carry the positive charge of the nucleus.

3. Which species has more electrons than neutrons? AO2 · L3 [1]

A $\ce{^{16}_{8}O^2-}$
B $\ce{^{19}_{9}F-}$
C $\ce{^{23}_{11}Na+}$
D $\ce{^{40}_{20}Ca^2+}$

4. State the relative mass and the relative charge of an electron. AO1 · L1 [2]

5. Describe how the mass and the charge of an atom are spread through it. AO1 · L1 [2]

6. An ion has 24 electrons and 30 neutrons, and a charge of 2+. Identify the ion and write its full symbol. AO2 · L2 [2]

7. Complete the table. AO2 · L2 [2]

species

protons

neutrons

electrons

$\ce{^{7}_{3}Li+}$

$\ce{^{31}_{15}P^3-}$

$\ce{^{65}_{29}Cu^2+}$

8. The ion $\ce{^{40}_{20}Ca^2+}$ and an ion $\ce{Q^3-}$ have the same number of electrons. The nucleon number of Q is 31. Deduce the identity of Q and the number of neutrons in one atom of Q. AO2 · L3 [2]

Answers

1. A. 31 protons, $71 - 31 = 40$ neutrons, $31 - 3 = 28$ electrons. B adds the charge to the electrons, as if a 3+ ion had gained electrons. C takes the nucleon number as the number of neutrons. D swaps the protons and neutrons. [1]

2. C. The nucleus is tiny but holds more than 99.9% of the mass and all the protons. A ignores the nucleus. B treats electrons as heavy: their total relative mass is about $11 \times \frac{1}{1836} = 0.006$ . D gives neutrons a charge; they are neutral. [1]

3. A. $\ce{O^2-}$ has 10 electrons and $16 - 8 = 8$ neutrons. B has 10 of each: equal, not more. C has 10 electrons and 12 neutrons. D has 18 electrons and 20 neutrons. The trap is the sign of the charge: a 2− ion has gained two electrons, so add 2. Subtracting gives $\ce{O^2-}$ only 6 electrons, and A is wrongly rejected. [1]

4. Relative mass $\frac{1}{1836}$ (accept about 0.0005 or "negligible") [1]; relative charge −1 [1].

5. M1: the mass is concentrated in the nucleus (in the protons and neutrons), which is very small [1]. M2: the positive charge is in the nucleus and the negative charge (electrons) is spread in shells around it [1]. Not enough: "the protons are in the middle" with nothing about mass.

6. M1: protons $= 24 + 2 = 26$ , so the element is iron [1]. M2: nucleon number $= 26 + 30 = 56$ , so the ion is $\ce{^{56}_{26}Fe^2+}$ [1].

7. $\ce{Li+}$ : 3, 4, 2. $\ce{P^3-}$ : 15, 16, 18. $\ce{Cu^2+}$ : 29, 36, 27. Two marks for all three rows correct; one mark for two rows correct [2]. The anion row is the one most often wrong: the 3− charge means three electrons gained.

8. M1: $\ce{Ca^2+}$ has $20 - 2 = 18$ electrons, so $\ce{Q^3-}$ has 18 electrons and $18 - 3 = 15$ protons: Q is phosphorus [1]. M2: neutrons $= 31 - 15 = 16$ [1]. Wrong: adding 3 to 18, which gives 21 protons and the wrong element.

The nuclear atom: particles, proton and nucleon numbers

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