Physics · 5 Nuclear physics

5.1.1 The atom

Before you start

There are positive and negative charges: like charges repel and opposite charges attract (4.2.1).
Charging by friction moves only electrons, never positive charge (4.2.1).
Reading numbers in standard form, such as $1 \times 10^{- 10}$ m.

Syllabus objectives covered (3)

Describe the structure of an atom in terms of a positively charged nucleus and negatively charged electrons in orbit around the nucleus
Know how atoms may form positive ions by losing electrons or form negative ions by gaining electrons
Describe how the scattering of alpha (α) particles by a sheet of thin metal supports the nuclear model of the atom, by providing evidence for: (a) a very small nucleus surrounded by mostly empty space (b) a nucleus containing most of the mass of the atom (c) a nucleus that is positively charged

Part 1 of 5

A nucleus with electrons in orbit

Every atom has two parts. At the centre is the nucleus, which is positively charged. Around it are the electrons, which are negatively charged.
The electrons are not stuck to the nucleus. They move in orbit around the nucleus, a long way out from it compared with the size of the nucleus itself.
Why do the electrons stay in orbit and not fly off? Opposite charges attract. The positive nucleus pulls on each negative electron, and that attraction holds the electron in its orbit.
A complete atom has no overall charge. The total negative charge of all its electrons is exactly equal in size to the positive charge of its nucleus, so the two cancel.
Electrons have very little mass. Almost all of the mass of an atom (more than 99.9%) is in the nucleus. You will see in this lesson how that was found out.
When you describe an atom, the trap is to name the parts but leave out the charges. The objective asks for three things: a positively charged nucleus, negatively charged electrons, and electrons in orbit around the nucleus. Say all three every time.

Part 2 of 5

Ions: move electrons, never the nucleus

An ion is an atom that has lost or gained electrons, so it now has an overall charge.
Only electrons are lost or gained. They are on the outside of the atom, so they are the part that can be pulled away or added. The nucleus at the centre does not change at all.
Losing electrons makes a positive ion. The nucleus still has all its positive charge, but there is now less negative charge to cancel it. The positive charge wins.
Gaining electrons makes a negative ion. The nucleus has the same positive charge as before, but there is now extra negative charge. The negative charge wins.
Notice the wording. A positive ion has not gained anything positive. It has lost negative charge. If you write 'it gains positive charge' or 'it gains protons', the mark is lost.
The size of the charge on the ion is the number of electrons moved. Write it as a multiple of the charge on one electron: lose 2 electrons and the charge is $+ 2$ ; gain 1 electron and the charge is $- 1$ .
To count the electrons in an ion, start from the number in the neutral atom. Subtract the number lost, or add the number gained.
$charge on ion = (electrons in neutral atom) - (electrons in ion)$
Check the sign with the formula. An atom with $11$ electrons that keeps only $10$ gives $11 - 10 = + 1$ . An atom with $17$ electrons that ends with $18$ gives $17 - 18 = - 1$ .
This is the same idea as charging by friction in 4.2.1. A rod that loses electrons becomes positive and a rod that gains electrons becomes negative. An ion is the same thing for a single atom.

Part 3 of 5

Firing alpha particles at thin metal foil

How do we know the atom has a tiny positive nucleus at all? The evidence comes from an experiment carried out by Geiger and Marsden, with the results explained by Rutherford.
They used alpha particles. For this lesson you need two facts about them: an alpha particle is positively charged, and it is thousands of times more massive than an electron. You will meet alpha particles properly in 5.2.
A radioactive source sent out a narrow beam of fast alpha particles. The beam was aimed at a very thin sheet of gold foil. Gold was chosen because it can be beaten into a very thin sheet.
The foil had to be thin for two reasons. Alpha particles are easily stopped, so a thick sheet would absorb them. And in a very thin sheet, an alpha particle is very unlikely to pass close to more than one nucleus, so each large deflection comes from a single encounter.
The whole apparatus was in a vacuum. Alpha particles are stopped by only a few centimetres of air, so with air present they would never reach the foil or the detector.
The detector was a small screen that gave a tiny flash of light each time an alpha particle hit it. The screen could be moved round the foil to count how many alpha particles came off at each angle.
apparatus diagram — not drawn yet
A box labelled 'vacuum' containing, on the left, a lead block with a narrow channel and an alpha source inside, sending a narrow beam to the right onto a thin vertical sheet labelled 'thin gold foil' at the centre; a circular dashed track around the foil carries a detector labelled 'detector (moves round)'; beyond the foil, many arrows continue straight on, two arrows leave at large angles, and one arrow returns back towards the source.
The detector moves round the foil. Most alpha particles go straight on, a few are deflected through large angles and a very small number come back.
Before this experiment, one idea of the atom was that its positive charge was spread evenly through the whole atom, with the electrons dotted through it. You do not need to learn this model. It is useful because it shows what result to expect if there were no nucleus.
With the positive charge spread thinly, the push on an alpha particle from any one place would be very weak. Every alpha particle would pass through with at most a very small deflection. None would be turned back.

Part 4 of 5

What the alpha particles actually did

There were three results. Learn them as a set, because each one is the evidence for a different feature of the nucleus.
Result 1: most alpha particles passed straight through the foil with no deflection, or with only a very small one.
Result 2: a small number were deflected through large angles.
Result 3: a very small number bounced back towards the source, deflected by more than $90 °$ .
Results 2 and 3 were the surprise. A model with the positive charge spread out cannot turn an alpha particle back at all. Something in the atom was strong enough, and heavy enough, to do it.
What decides the deflection is how close an alpha particle passes to a nucleus. Far away: no deflection. Close by: pushed away along a curved path through a large angle. Aimed straight at it: slowed, stopped and sent back the way it came.
forces diagram — not drawn yet
A small dot labelled 'nucleus (+)' in the middle of the page; four alpha particles labelled 'α (+)' approach from the left along parallel horizontal lines: the one far above and the one far below the nucleus continue in straight lines; one passing just above the nucleus curves smoothly upwards and away, leaving at a large angle, with a short arrow at its closest point labelled 'repulsive force' pointing away from the nucleus; the one aimed at the centre of the nucleus stops before reaching the dot and returns to the left along the same line.
The closer an alpha particle passes to the nucleus, the larger its deflection. The force on it always points away from the nucleus.
Notice that the alpha particle never touches the nucleus. It is pushed away by the repulsion between the two positive charges before it gets there. So the right word is repelled, not 'hit' or 'collided with'.

Part 5 of 5

Three conclusions about the nucleus

Each conclusion comes from a particular result. A mark for a conclusion depends on the evidence you link it to, so keep the pairs together.
(a) A very small nucleus surrounded by mostly empty space. Most alpha particles went straight through. They never came near anything that could push them, so most of each atom must be empty space.
Only a small number were deflected through large angles. So only a small number passed close to whatever does the pushing. That means it is a very small target compared with the whole atom: a very small nucleus.
Write 'mostly empty space', not 'empty space'. The atom also contains the nucleus and the electrons.
(b) A nucleus containing most of the mass of the atom. Some alpha particles were turned back. A light object cannot reverse a heavy moving one. Picture a tennis ball rolling into a bowling ball: the tennis ball bounces back, the bowling ball barely moves. To turn back an alpha particle, the nucleus must be much more massive than the alpha particle.
The electrons cannot be what turns them back. Each electron is thousands of times less massive than an alpha particle, so the alpha particle pushes straight past it. The mass must be concentrated in the nucleus.
(c) A nucleus that is positively charged. The deflected alpha particles were pushed away from the nucleus, and the ones aimed straight at it were turned back. That is repulsion.
Alpha particles are positive, and like charges repel. So the nucleus must be positively charged too.
Put (a), (b) and (c) together and you have the nuclear model from the first section: a tiny, massive, positive nucleus at the centre, with the negative electrons in orbit around it.
How small is 'very small'? The diameter of a nucleus is tens of thousands of times smaller than the diameter of its atom. If a question gives you the two sizes, divide the atom's diameter by the nucleus's diameter to find how many times bigger the atom is.

Worked examples

Example 1. A sulfur atom has $16$ electrons. It gains $2$ electrons. Determine whether a positive or a negative ion forms, the number of electrons in the ion and the charge on the ion.

Show the working

Decide the sign first. The atom has gained electrons, so it now has more negative charge than the positive charge of its nucleus. A negative ion forms.
Count the electrons. Gaining adds to the number in the neutral atom.
$16 + 2 = 18 electrons$
Find the charge with the rule from the lesson: electrons in the neutral atom minus electrons in the ion.
$16 - 18 = - 2$
Check that it makes sense. The nucleus has not changed, so its positive charge still balances $16$ electrons. There are $2$ extra electrons with nothing to cancel them, so the charge is $- 2$ .

Answer: A negative ion, with $18$ electrons and a charge of $- 2$ (twice the charge of one electron).

Example 2. In an alpha-particle scattering experiment with thin gold foil, most alpha particles pass straight through, a small number are deflected through large angles and a very small number bounce back. Explain how these results provide evidence for (a) a very small nucleus surrounded by mostly empty space, (b) a nucleus containing most of the mass of the atom and (c) a nucleus that is positively charged.

Show the working

Take each feature in turn and give it its own result. An Explain needs the result and the reason, not just the conclusion.
(a) Most alpha particles pass straight through, so most of the atom is empty space. Only a small number are deflected through large angles, so only a few pass close to the nucleus: the nucleus is very small compared with the atom.
(b) Some alpha particles bounce back. Only something much more massive than an alpha particle can reverse its direction, so the mass of the atom must be concentrated in the nucleus. The electrons are far too light to do this.
(c) The alpha particles that pass close to the nucleus are repelled, pushed away from it. Alpha particles are positive and like charges repel, so the nucleus is positive.
Check every conclusion has its result attached. 'The nucleus is positive' on its own gives no evidence. 'The alpha particles are repelled, and like charges repel' does.

Answer: (a) Most pass straight through, so the atom is mostly empty space; only a few are deflected through large angles, so the nucleus is very small. (b) Some bounce back, which needs something much more massive than an alpha particle, so most of the mass is in the nucleus. (c) Alpha particles are repelled by the nucleus, and they are positive, so the nucleus is positive.

Example 3. A typical atom has a diameter of about $1.0 \times 10^{- 10}$ m. Its nucleus has a diameter of about $1.0 \times 10^{- 15}$ m. (a) Calculate how many times larger the diameter of the atom is than the diameter of the nucleus. (b) In a model, the nucleus is drawn as a dot $1$ mm across. Calculate how wide the atom must be in the model. (c) Comment on what your answer tells you about the alpha-scattering results.

Show the working

(a) 'How many times larger' means divide the bigger size by the smaller one. Both are in metres, so the units cancel and the answer is just a number.
$\frac{1.0 \times 10^{- 10}}{1.0 \times 10^{- 15}} = 1.0 \times 10^{5}$
With powers of ten, dividing means subtracting the indices: $- 10 - (- 15) = 5$ . So the atom is $100 000$ times wider.
(b) Every length in the model is scaled by the same factor, so multiply the nucleus size by $1.0 \times 10^{5}$ .
$1 mm \times 1.0 \times 10^{5} = 1.0 \times 10^{5} mm$
Convert to a size you can picture. There are $1000$ mm in $1$ m, so $1.0 \times 10^{5}$ mm is $100$ m.
(c) A dot $1$ mm across in the middle of a space $100$ m wide is a very small target. An alpha particle fired through such an atom is very unlikely to pass close to the nucleus. That is why most alpha particles pass straight through.

Answer: (a) $1.0 \times 10^{5}$ times (no unit). (b) $100$ m. (c) The nucleus is a tiny target in a mostly empty atom, so most alpha particles miss it and pass straight through.

Where people go wrong

Mistake: Writing that a positive ion forms when an atom gains protons or gains positive charge.

Instead: A positive ion forms when an atom loses electrons. The nucleus does not change.

Only the electrons, on the outside of the atom, are lost or gained. The positive charge was always there. Losing electrons just leaves less negative charge to cancel it.

Mistake: Saying the alpha particles that come back 'hit the nucleus and bounce off'.

Instead: Say the alpha particles are repelled by the nucleus, because both are positive.

The alpha particle is turned back by the repulsion before it reaches the nucleus. 'Repelled' is the word that links the result to the positive charge of the nucleus. 'Hit' gives no evidence about charge.

Mistake: Matching a result to the wrong conclusion, for example 'most went straight through, so the nucleus is positive'.

Instead: Straight through gives mostly empty space; large deflections by a few give a very small nucleus; repulsion gives a positive nucleus; bouncing back gives most of the mass in the nucleus.

Particles that go straight through feel no force at all, so they tell you nothing about charge. Each conclusion needs the result that actually supports it.

Mistake: Writing that the atom is 'empty space'.

Instead: Write that the atom is 'mostly empty space'.

The atom contains a nucleus and electrons. 'Empty' on its own is wrong physics and contradicts the nucleus you are describing.

Mistake: Describing an atom as 'a nucleus with electrons around it' without the charges.

Instead: Say a positively charged nucleus, with negatively charged electrons in orbit around it.

The objective is about the charges as well as the parts. A description without 'positive' and 'negative' leaves out what the objective asks for.

Check yourself

State the charge on the nucleus and the charge on an electron.
Answer
The nucleus is positively charged. An electron is negatively charged.
Explain why the electrons stay in orbit around the nucleus.
Answer
The nucleus is positive and the electrons are negative. Opposite charges attract, so the nucleus pulls on each electron and holds it in orbit.
An aluminium atom has $13$ electrons. It loses $3$ electrons. State the type of ion formed, the number of electrons in it and its charge.
Answer
A positive ion, with $13 - 3 = 10$ electrons and a charge of $+ 3$ .
An ion has a charge of $- 1$ and contains $18$ electrons. Deduce how many electrons the neutral atom had.
Answer
A charge of $- 1$ means the atom gained $1$ electron, so the neutral atom had $18 - 1 = 17$ electrons.
Most alpha particles pass straight through thin gold foil. State what this result shows about the atom.
Answer
The atom is mostly empty space (and the nucleus is very small, so most alpha particles do not pass near it).
Explain why the electrons in the gold atoms cannot be what turns some alpha particles back.
Answer
Electrons are thousands of times less massive than alpha particles. A very light object cannot reverse a much heavier one, so the alpha particles push straight past the electrons.
Suggest why the alpha-scattering experiment is done with a very thin sheet of metal.
Answer
Alpha particles are easily stopped, so a thick sheet would absorb them. A thin sheet lets them pass through, and each one is unlikely to pass close to more than one nucleus.
In a scale model, the nucleus is a bead $5$ mm across and the atom is $100 000$ times wider than the nucleus. Calculate the width of the atom in the model, in metres.
Answer
$5 \times 100 000 = 500 000$ mm, which is $500 000 \div 1000 = 500$ m.

Exam questions

Try each part first. Open the mark scheme after you have written your answer.

Question 1. An atom of magnesium has $12$ electrons.

(a) Describe the structure of an atom. 3 marks No calculator

Mark scheme

B1 a nucleus at the centre that is positively charged
B1 electrons that are negatively charged
B1 the electrons are in orbit around the nucleus

(b) Explain why the magnesium atom has no overall charge. 2 marks No calculator

Mark scheme

B1 the nucleus is positive and the electrons are negative
B1 the total negative charge of the 12 electrons is equal in size to the positive charge of the nucleus, so they cancel, owtte; accept 'the number of protons (12) equals the number of electrons (12)'

(c) The magnesium atom loses $2$ electrons and forms an ion. Determine the charge on the ion and the number of electrons in it. 2 marks No calculator

Mark scheme

B1 +2 / 2+ / +2e / +3.2 × 10⁻¹⁹ C (twice the size of the charge on one electron); sign required; 'positive' without the size is insufficient
B1 10 electrons

Question 2. In a vacuum, a narrow beam of alpha particles is aimed at a very thin sheet of gold foil. A detector is moved around the foil to count the alpha particles leaving it at different angles. Alpha particles are positively charged.

(a) Most of the alpha particles pass straight through the foil and only a small number are deflected through large angles. Explain what these results show about the structure of the atom. 2 marks No calculator

Mark scheme

B1 the atom is mostly empty space; 'the atom is empty space' alone is insufficient
B1 the nucleus is very small (so few alpha particles pass close to it)

(b) Explain how the deflection of the alpha particles shows that the nucleus is positively charged. 2 marks No calculator

Mark scheme

B1 the alpha particles are repelled by / pushed away from the nucleus
B1 like charges repel and alpha particles are positive, so the nucleus is positive

(c) A very small number of alpha particles are deflected back towards the source. Explain how this shows that the nucleus contains most of the mass of the atom. 2 marks No calculator

Mark scheme

B1 to reverse the direction of an alpha particle, the nucleus must be much more massive than the alpha particle, owtte
B1 so (most of) the mass of the atom is concentrated in the (very small) nucleus / the nucleus is very dense, owtte; accept 'electrons are far too light to turn back an alpha particle, so the mass must be in the nucleus'

(d) Suggest why the gold foil must be very thin. 1 mark No calculator

Mark scheme

B1 so the alpha particles are not absorbed / can pass through the foil; or so each alpha particle is unlikely to be deflected by more than one nucleus

(e) Suggest why the experiment is carried out in a vacuum. 1 mark No calculator

Mark scheme

B1 alpha particles are stopped / absorbed by a few centimetres of air; accept 'so the alpha particles are not deflected / scattered by air molecules', owtte

Question 3. A student makes a scale model of an atom. In the model, the nucleus is a ball of diameter $2.0$ cm. For the atom being modelled, the diameter of the atom is $50 000$ times the diameter of its nucleus.

(a) Calculate the diameter of the atom in the model. Give your answer in metres. 2 marks

Mark scheme

C1 2.0 × 50 000 = 100 000 cm / 1.0 × 10⁵ cm seen, or an equivalent in other units (e.g. 0.020 m × 50 000)
A1 1000 m / 1.0 × 10³ m; unit required

(b) Three alpha particles, P, Q and R, travel towards a single gold nucleus along parallel lines. P is aimed directly at the centre of the nucleus. Q passes very close to the nucleus. R passes far from the nucleus. Predict the path of each alpha particle. 3 marks No calculator

Mark scheme

B1 P is turned back / returns along its original path towards the source
B1 Q is deflected through a large angle, away from the nucleus
B1 R continues in a straight line / is not deflected (or only very slightly)

How this is examined

Linking each alpha-scattering result to the feature of the nucleus it supports: an Explain worth about two marks for each feature: you are given a result, or asked for one, and must say what it shows Result and conclusion together, for each feature: 'most went straight through, so the atom is mostly empty space; few deflected through large angles, so the nucleus is very small'; 'some bounced back, so the nucleus is much more massive than an alpha particle / contains most of the mass'; 'alpha particles were repelled, and like charges repel, so the nucleus is positive'.
Describing the structure of an atom with both charges named: a two- or three-mark Describe, or a labelled Sketch of an atom Three separate points: 'a positively charged nucleus at the centre'; 'negatively charged electrons'; 'the electrons orbit the nucleus'. For the atom having no overall charge: 'the total negative charge of the electrons equals the positive charge of the nucleus'.
Saying how an ion forms, and finding its charge and number of electrons: a one- or two-mark State or Determine about a named atom losing or gaining electrons 'Loses electrons, so a positive ion' or 'gains electrons, so a negative ion'; the charge with its sign, equal to the number of electrons moved (for example $+ 2$ ); the new number of electrons, found by subtracting the number lost or adding the number gained. Electrons must be named: 'gains protons' scores nothing.
Predicting the path of an alpha particle from how close it passes to a nucleus: a Predict or Sketch about alpha particles aimed at a nucleus at different distances Far away: straight on, no deflection. Close: a curved path away from the nucleus, through a large angle. Head-on: comes back along its own path. Every deflection is away from the nucleus.
Why the metal is thin and why the apparatus is in a vacuum: a one-mark Suggest about the set-up Thin: 'so the alpha particles are not absorbed / can pass through the foil'. Vacuum: 'alpha particles are stopped (absorbed) by a few centimetres of air'.

Words to know

Atom: A positively charged nucleus with negatively charged electrons in orbit around it. A complete atom has no overall charge.
Nucleus: The very small, positively charged centre of an atom, which contains almost all of its mass.
Electron: A negatively charged particle with very little mass, in orbit around the nucleus.
Ion: An atom that has lost or gained electrons, so it has an overall charge.
Positive ion: An ion formed when an atom loses one or more electrons.
Negative ion: An ion formed when an atom gains one or more electrons.
Alpha particle: A positively charged particle given out by some radioactive sources, thousands of times more massive than an electron.
Alpha-particle scattering: The deflection of alpha particles as they pass through thin metal foil, which gives the evidence for the nuclear model of the atom.
Nuclear model: The model of the atom with a very small, massive, positively charged nucleus at the centre, surrounded by mostly empty space in which the electrons orbit.

All Physics lessons Next: 5.1.2 The nucleus