PhysicsCore20 min read

The Nuclear Model of the Atom

Protons, neutrons, electrons, isotopes and the experiment that found the nucleus

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01

How we know the atom is mostly empty

By 1909 the accepted picture of the atom was Thomson's: a ball of positive charge with electrons embedded in it, like currants in a bun. Geiger and Marsden set out to test it by firing alpha particles at a very thin sheet of gold foil and recording where they went.

If the plum-pudding model were right, the positive charge would be spread thinly across the whole atom and every alpha particle should have sailed through with at most a slight nudge. That is not what happened.

Almost all the alpha particles did pass straight through — but a very small fraction were deflected through large angles, and a handful came almost straight back. Rutherford said it was as astonishing as firing a shell at tissue paper and having it bounce back at you.

ObservationWhat it proves
Most particles pass straight throughthe atom is mostly empty space
A few deflect through large anglesthere is a concentrated region of positive charge that repels them
A very few bounce almost straight backthat region is extremely small and very massive

Pair each observation with its conclusion

This question is asked constantly, and the marks are awarded for the link. Listing the three observations and then listing the three conclusions separately usually loses marks, because the examiner cannot see which supports which. Write them as pairs.

02

The nuclear model

Definition

Nucleus — The tiny, dense, positively charged centre of an atom, containing protons and neutrons and almost all of the atom's mass.

Rutherford's conclusion was the model still used today. An atom has a minute nucleus at its centre carrying all the positive charge and nearly all the mass, with electrons occupying the huge volume around it.

The scale is hard to take in. A nucleus is roughly 10⁻¹⁵ m across and an atom about 10⁻¹⁰ m — a factor of a hundred thousand. If a nucleus were a marble on the centre spot of a cricket ground, the nearest electrons would be out beyond the boundary, and everything between would be empty.

That emptiness is why most alpha particles went straight through the foil, even though the foil was thousands of atoms thick. The foil had to be extremely thin for a different reason: so that each alpha particle would meet at most one nucleus, and the deflections could be interpreted.

nucleus ≈ 10⁻¹⁵ matom ≈ 10⁻¹⁰ mthe atom is about 100 000 times wider than its nucleus

The nucleus is drawn far too large to be seen at all at true scale. Notice that adding protons pulls the electrons into tighter shells — more positive charge at the centre means a stronger pull on every electron.

03

Protons, neutrons and electrons

Three particles account for every atom. The proton carries a charge of +1 and a mass of 1 on the atomic scale. The neutron has almost the same mass but no charge at all. The electron carries a charge of −1 and a mass roughly 1/1836 of a proton — small enough that it is normally ignored when working out the mass of an atom.

Protons and neutrons together are called nucleons, because they are the particles found in the nucleus. A neutral atom has equal numbers of protons and electrons, so the charges cancel exactly.

The nucleus is held together by the strong nuclear force, which acts between nucleons over very short distances and is powerful enough to overcome the electrostatic repulsion between the protons packed inside it. Without it no nucleus with more than one proton could exist.

ParticleRelative chargeRelative massWhere it is
Proton+11in the nucleus
Neutron01in the nucleus
Electron−11/1836 (≈ 0)in shells around the nucleus
04

Nuclide notation

A nucleus is described by two numbers. The proton number Z, also called the atomic number, counts the protons. It alone decides which element the atom is: every carbon nucleus has six protons, and anything with six protons is carbon.

The nucleon number A, also called the mass number, counts protons and neutrons together. The number of neutrons is therefore A − Z, which is worth writing down explicitly because questions ask for it directly.

These are written around the chemical symbol, with the nucleon number above and the proton number below.

ᴬ𝗓XA = Z + NN = A − ZA is the nucleon number, Z the proton number, N the number of neutrons
A
nucleon (mass) number
Z
proton (atomic) number
N
neutrons
Worked example 14 marks

A nuclide is written as ²³⁵₉₂U. State the number of protons, neutrons and electrons in a neutral atom of it, and explain what the number 235 represents.

  1. The lower number is the proton number, so there are 92 protons.92 protons is what makes it uranium.
  2. A neutral atom has equal protons and electrons, so 92 electrons.The charges must cancel.
  3. Neutrons = A − Z = 235 − 92, so 143 neutrons.Subtracting is the step examiners look for.
  4. 235 is the nucleon number — the total number of protons and neutrons.Not the number of neutrons, and not the mass in any real unit.

92 protons, 143 neutrons, 92 electrons

05

Isotopes

Definition

Isotopes — Atoms of the same element — so the same number of protons — with different numbers of neutrons, and therefore different nucleon numbers.

Change the number of neutrons and you have not changed the element, because the element is fixed by the proton number. You have made an isotope of it. Carbon-12 and carbon-14 both have six protons; one has six neutrons and the other eight.

Isotopes of an element are chemically identical. Chemistry is decided entirely by the electrons, and the number of electrons follows the number of protons, which has not changed. This is why carbon-14 is taken up by living things exactly as ordinary carbon is — which is what makes radiocarbon dating possible.

Their nuclear properties can differ completely. Some isotopes have a stable balance of protons and neutrons and last forever; others do not, and those decay radioactively. Uranium-235 will sustain a chain reaction and uranium-238 will not, even though they are the same element.

Key points

  1. Proton number decides the element; nucleon number decides the isotope.
  2. Isotopes have the same chemistry because they have the same electrons.
  3. Isotopes can have completely different nuclear stability.
  4. Neutron count is A − Z, never read straight off the symbol.
  5. The nucleus holds nearly all the mass; the electrons hold almost none.
06

Fundamental particles

Protons and neutrons are not fundamental — they are built from quarks. A proton is two up quarks and a down; a neutron is one up and two downs. Only up and down quarks are needed at this level, and their fractional charges are what produce the whole-number charges we observe.

Electrons, by contrast, appear to be genuinely fundamental. They belong to a family called leptons, which also includes the neutrino. Quarks feel the strong nuclear force; leptons do not, and that difference is what separates the two families.

ParticleCompositionCharge
up quark (u)fundamental+⅔ e
down quark (d)fundamental−⅓ e
protonuud+1 e
neutronudd0
electronfundamental (a lepton)−1 e
neutrinofundamental (a lepton)0
Worked example

Show that the quark composition of a neutron gives the correct charge, and describe what happens to the quarks during beta-minus decay.

  1. A neutron is udd: charge = +⅔ − ⅓ − ⅓.Adding the fractional charges of the three constituent quarks.
  2. = 0, as required.The fractions cancel exactly, which is why the neutron is neutral.
  3. In beta-minus decay a neutron becomes a proton, so udd becomes uud.Comparing the two compositions shows exactly one quark has changed.
  4. A down quark has changed into an up quark, emitting an electron and an antineutrino.Charge is conserved overall: the +1 of the new proton is balanced by the −1 of the emitted electron.

udd gives zero charge; in β⁻ decay a down quark becomes an up quark

Why fractional charges are never observed alone

No experiment has ever detected an isolated quark. They are permanently bound in groups whose charges add to whole multiples of e, which is why every particle we can actually detect carries a whole-number charge. Beta decay is the clearest evidence that quarks exist at all — something inside the neutron has to change for it to become a proton.

Practice questions

6 questions · 27 marks · full working on every one

Try each one on paper first, then open the working. The marks are shown where they are actually awarded, because that is where they are actually lost.

Short questions

2 · 4 marks

Two marks each, in the style of the short-question section of the paper. Answer in two or three lines.

SQ1[2 marks]
State what is meant by the nucleon number and the proton number of a nuclide.
Model answer

The nucleon number A is the total number of protons and neutrons in the nucleus. The proton number Z is the number of protons alone.

Examiner tip. Nucleon number counts both; proton number counts one. Say both explicitly.

SQ2[2 marks]
Explain why isotopes of the same element have identical chemical properties.
Model answer

They have the same number of protons and therefore the same number of electrons in the same arrangement. Chemical behaviour is decided by the electrons, not by the number of neutrons.

Examiner tip. The chain is proton number → electron arrangement → chemistry. Missing the middle step loses the mark.

Long questions

1 · 8 marks

Theory and numerical together, as they appear in the long-question section.

LQ1[8 marks]
In the Geiger–Marsden experiment, alpha particles were fired at a very thin gold foil.
  1. State the two observations that were made. [2]
  2. Explain what each observation shows about the structure of the atom. [4]
  3. Explain why the foil had to be extremely thin. [2]
Mark scheme
  1. Almost all the alpha particles passed straight through[1]
  2. A very small fraction were deflected through large angles, some straight back[1]
  3. Passing straight through shows the atom is mostly empty space[1]
  4. Large deflections show a concentrated region of positive charge[1]
  5. Which repels the positive alpha particle[1]
  6. Backward scattering shows that region is also very massive, and very small[1]
  7. So each alpha particle meets at most one nucleus[1]
  8. A thicker foil would cause multiple scattering and the result could not be interpreted[1]

Examiner tip. Each observation must be paired with the conclusion it supports. Listing the observations and then listing the conclusions separately usually loses marks, because the examiner cannot see which supports which.

Exam questions

3 · 15 marks

Multi-part questions with a full mark scheme.

Q1[6 marks]
An atom is represented as ²³⁵₉₂U.
  1. State the number of protons, neutrons and electrons in a neutral atom of this isotope.
  2. Another isotope is ²³⁸₉₂U. State what is the same and what is different about it.
  3. Explain why the two isotopes behave identically in chemical reactions.
Mark scheme
  1. 92 protonsthe proton number[1]
  2. 235 − 92 = 143 neutrons[1]
  3. 92 electrons, since the atom is neutral[1]
  4. Same number of protons (92); different number of neutrons (146 instead of 143)[1]
  5. Chemical behaviour depends on the electrons[1]
  6. Both have 92 electrons arranged identically, so they react in the same way[1]

(a) 92 p, 143 n, 92 e (b) same Z, different A (c) identical electron arrangement

Examiner tip. Neutrons are always A − Z. Writing that subtraction down explicitly earns the mark even if the arithmetic then slips.

Q2[6 marks]
In the alpha-scattering experiment, alpha particles were directed at a thin gold foil.
  1. State the three main observations.
  2. State the conclusion drawn from each.
Mark scheme
  1. Most alpha particles passed straight through[1]
  2. So the atom is mostly empty space[1]
  3. Some were deflected through large angles[1]
  4. So there is a concentrated positive charge repelling them[1]
  5. A very few were reflected almost straight back[1]
  6. So the nucleus is very small and contains most of the atom's mass[1]

Examiner tip. Pair each observation with its conclusion. Listing three observations and then three conclusions separately still works, but pairing them makes it obvious to the examiner that you know which goes with which.

Q3[3 marks]
Explain why the plum-pudding model could not account for the results of the alpha-scattering experiment.
Mark scheme
  1. In that model the positive charge is spread thinly throughout the atom[1]
  2. So the repulsive force on an alpha particle anywhere would be small[1]
  3. It could not produce the large-angle deflections or backscattering that were observed[1]