E.1 Concept Builder Part 1 · HL Physics Notebook

1. Start with predictions

7 minPairs

ATL Thinking: predict and justify. Social: compare with a partner. You will test every prediction later with a simulation.

1.1A beam of alpha particles is fired at a gold foil only a few hundred atoms thick, in a vacuum. Most of the alpha particles…

A. pass straight through, or almost straight B. bounce back C. are stopped inside the foil

You test it in stage 2.

1.2The gold foil (Z = 79) is replaced by an aluminium foil (Z = 13) with the same number of atoms in the beam’s path. The number of alpha particles deflected through large angles…

A. increases B. decreases C. stays the same

You test it in stage 3.

1.3Carbon-12 and carbon-14 are both carbon. Their nuclei have different numbers of…

A. protons B. neutrons C. electrons

You test it in stage 4.

1.4Imagine a gold atom blown up to the size of a football stadium (about 140 m across). Its nucleus would be about the size of…

A. a football (about 20 cm) B. a pea (about 7 mm) C. a grain of fine sand (about 0.1 mm)

You test it in stage 5.

1.5Explain the reasons for one of your predictions.

What a good answer looks like

A good reason uses an idea, for example: “Most of the atom is…, so…” or “The electric force depends on the charge, so…”. You will see in the simulations which reasons hold.

2. The gold foil: test prediction 1.1

18 minPairs → individual

ATL Research: interpret experimental results. Thinking: link evidence to a model.

Simulation A · Alpha particles and a gold nucleus each alpha particle is aimed at a random point of the atom; the drawing makes the nucleus much bigger than it really is

fired0

deflected more than 10°0

bounced back (more than 90°)0

The electric force (from D.2) F = kq₁q₂/r² Alpha particle q₁ = +2e; gold nucleus q₂ = +79e; k = 8.99 × 10⁹ N m² C⁻². The force grows very fast as r gets small.

2.1Fire 500 alpha particles. Which statement matches the counters?

most go almost straight through; a few are deflected a lot; very few bounce back about half bounce back all are deflected by about the same angle

2.2An alpha particle is 1.0 × 10⁻¹⁴ m from a gold nucleus. The repulsive force on it, F =

N

2.3In the Thomson model the same +79e charge is spread through the whole atom (radius 1.4 × 10⁻¹⁰ m). The biggest force it can give is at its edge, F =

N

Back check

2.bBack check: the force from the tiny nucleus is how many times bigger than the biggest Thomson force?

What the three results tell us

Most alpha particles go straight through → the atom is mostly empty space.
A few are deflected through large angles → a very large repulsive force, so the positive charge is in a very small region.
Very few bounce back → that region is tiny and contains most of the mass: the nucleus.

Find the mistake

A student explains why a few alpha particles bounce back:

“They hit the gold nucleus and bounce off it, like a ball off a wall.”

What is wrong?

They never touch the nucleus: the electric repulsion slows them and turns them round before they reach it. They hit the electrons, not the nucleus. Nothing is wrong.

Hinge question

Choose your answer. You will see at once if it is right, and why.

Why must the gold foil be very thin?

A. so that each alpha particle is deflected by at most one nucleus B. so that the foil does not melt C. so that the electrons can escape

2.4Was prediction 1.1 right? Explain what it tells us about the atom.

What a good answer looks like

A, most go straight through. In the simulation almost all of the 500 paths were (nearly) straight, because most of the atom is empty space: an alpha particle that does not pass close to the nucleus feels almost no force. Only the few that pass very close to the tiny, positive nucleus feel a large force (364 N at 1.0 × 10⁻¹⁴ m) and are deflected a lot.

3. Which model? Test prediction 1.2

15 minPairs → individual

ATL Thinking: compare models with the same evidence. Communication: use the correct key words.

Simulation B · Change the target same alpha particles, same number fired; compare gold, aluminium and the Thomson model of gold

fired0

deflected more than 10°0

bounced back (more than 90°)0

Nuclear charge q₂ = +Ze Gold Z = 79, aluminium Z = 13. At the same distance, F ∝ Z. In the Thomson model the positive charge is spread through the whole atom, with the electrons inside it.

3.1Choose “Thomson model (gold)” and fire 500. How many bounce back?

none: every path is bent only a little about the same number as with a gold nucleus more than with a gold nucleus

3.2An alpha particle is 1.0 × 10⁻¹⁴ m from an aluminium nucleus (Z = 13). F =

N

3.3At the same distance, the force from a gold nucleus is how many times the force from an aluminium nucleus?

3.4An alpha particle has about 7000 times the mass of an electron. What does this tell us about the large deflections?

electrons are far too light to push an alpha particle aside, so the deflections come from something heavy and positive the electrons cause the large deflections the alpha particles must be slow

Find the mistake

A student explains the result with aluminium:

“Fewer alpha particles bounce back because the aluminium nucleus is smaller, so it is harder to hit.”

What is wrong?

The alpha particles do not hit the nucleus. The aluminium nucleus has a smaller charge (+13e), so the repulsion is weaker and fewer are turned through large angles. The aluminium nucleus is bigger. Nothing is wrong.

Hinge question

Choose your answer. You will see at once if it is right, and why.

Why is the experiment done in a vacuum?

A. so that air molecules do not slow down or deflect the alpha particles B. so that the gold does not rust C. so that the alpha particles are attracted to the foil

What if? · stretch

3.wThe alpha particles have 5.0 MeV of kinetic energy. In joules, E =

J

3.5Was prediction 1.2 right? Explain with the force.

What a good answer looks like

B, it decreases. The aluminium nucleus has a charge of +13e instead of +79e, so at the same distance the repulsion is about 6 times weaker (60 N instead of 364 N at 1.0 × 10⁻¹⁴ m). Fewer alpha particles are turned through large angles. In the simulation the counters for large deflections and bounce-backs were much smaller than for gold.

4. Nuclear notation: test prediction 1.3

15 minIndividual

ATL Self-management: use the notation accurately. Thinking: separate what defines an element from what does not.

Simulation C · Build an atom choose the numbers of protons, neutrons and electrons

protons Z 6neutrons N 6electrons 6

nucleon number A—

element—

charge of the atom—

Nuclear notation ^A_ZX Z = proton number (number of protons), A = nucleon number (protons + neutrons), N = A − Z neutrons. A neutral atom has Z electrons. Isotopes: same Z, different numbers of neutrons.

4.1A gold nucleus is ¹⁹⁷₇₉Au. Number of neutrons =

neutrons

4.2Number of electrons in the ion Au³⁺ =

electrons

4.3Set Z = 6 and change N from 6 to 8. What changes?

A changes from 12 to 14, but it is still carbon: an isotope it becomes a different element the charge of the atom changes

4.4Nucleon number A of a nucleus with 6 protons and 8 neutrons =

Find the mistake

A student reads the nucleus ²³₁₁Na:

“Sodium has 23 neutrons.”

What is wrong?

23 is the nucleon number A. Neutrons N = A − Z = 23 − 11 = 12. Sodium has 11 neutrons. Nothing is wrong.

Hinge question

Choose your answer. You will see at once if it is right, and why.

An atom becomes the ion X²⁻. What has changed?

A. it has gained 2 electrons; the nucleus is the same B. it has lost 2 protons C. it has gained 2 neutrons

Back check

4.bBack check: uranium-238 has Z = 92. Number of neutrons =

neutrons

4.5Was prediction 1.3 right? Explain with Z and A.

What a good answer looks like

B, neutrons. Both are carbon, so both have Z = 6 protons (the element is set by Z), and as neutral atoms both have 6 electrons. Carbon-12 has 12 − 6 = 6 neutrons and carbon-14 has 14 − 6 = 8 neutrons. Nuclei with the same Z and different numbers of neutrons are isotopes.

5. Sizes: test prediction 1.4

15 minPairs → individual

ATL Thinking: use scale and powers of ten. Communication: explain with a model.

Simulation D · Zoom into a gold atom move the slider to the right to zoom in, by powers of ten

width of the view 1 × 10⁻⁹ m

radius of the atom1.4 × 10⁻¹⁰ m

radius of the nucleus7.0 × 10⁻¹⁵ m

atom ÷ nucleus2.0 × 10⁴

Sizes atom: about 10⁻¹⁰ m · nucleus: about 10⁻¹⁵ m (1 fm = 10⁻¹⁵ m). Gold: atom radius 1.4 × 10⁻¹⁰ m, nucleus radius 7.0 × 10⁻¹⁵ m.

5.1Radius of the gold atom ÷ radius of its nucleus =

5.2Scale the atom up to 140 m. The nucleus would be how many millimetres across?

mm

5.3What fraction of the atom’s volume is the nucleus?

Find the mistake

A student compares the atom and the nucleus:

“The nucleus is 10⁵ times smaller, so it takes up 1/10⁵ of the atom’s volume.”

What is wrong?

10⁵ is the ratio of the RADII. Volume goes as r³, so the nucleus takes up about 1/10¹⁵ of the volume. The nucleus is 10⁵ times bigger. Nothing is wrong.

Where is the mass?

The 79 electrons of gold have a mass of 79 × 9.11 × 10⁻³¹ kg.
The nucleus (197 nucleons) has a mass of about 197 × 1.66 × 10⁻²⁷ kg.
So almost all of the mass is in the nucleus, in about 10⁻¹³ of the volume.

Back check

5.bBack check: mass of the electrons ÷ mass of the nucleus =

5.4Where is most of the mass of an atom?

in the nucleus in the electrons spread evenly through the atom

5.5Was prediction 1.4 right? Explain with numbers.

What a good answer looks like

B, a pea. The gold atom is about 2.0 × 10⁴ times wider than its nucleus (1.4 × 10⁻¹⁰ m ÷ 7.0 × 10⁻¹⁵ m). Scaled to 140 m, the nucleus is 140/2.0 × 10⁴ = 7 mm across. That is why most alpha particles pass straight through: the atom is mostly empty space.

6. Show it, then reflect

10 minIndividual

ATL Communication + Self-management: choose how to show your understanding, retrieve without notes, plan your next step.

Success criteria: your answer must…

state the three results of the experiment;
link each result to one conclusion about the atom;
say why the Thomson model cannot explain the bounce-backs;
use one number from a simulation today.

Option A · Written

One paragraph: “How the gold foil experiment showed that the atom has a small, dense, positive nucleus.”

Option B · Sketch

Draw three alpha particle paths near a nucleus (far, close, head-on), and label which result each one explains.

Option C · Spoken

Explain to your partner in 1 minute why the Thomson model fails. Your partner ticks the success criteria.

6.1Write your paragraph or your notes.

What a good answer looks like

Model answer (Option A): Alpha particles were fired at a very thin gold foil in a vacuum. Most went straight through, so the atom is mostly empty space. A few were deflected through large angles and a very small number bounced back. This needs a very large repulsive force, which a spread-out (Thomson) charge cannot give: the force from the whole atom’s charge at its edge is only about 2 × 10⁻⁶ N, but a nucleus gives 364 N at 1.0 × 10⁻¹⁴ m. So the positive charge, and most of the mass, must be in a very small region at the centre: the nucleus, about 10⁻¹⁵ m across, with the electrons far away.

Exit ticket (no notes)

1How many neutrons are in the nucleus ²³⁸₉₂U?

2Oxygen has Z = 8. How many electrons are in the ion O²⁻?

3Most alpha particles pass straight through a gold foil. This shows that…

the atom is mostly empty space the nucleus is negative gold atoms are very large

4A very small number of alpha particles bounce back. This shows that…

the electrons are heavy the positive charge and most of the mass are in a tiny nucleus the alpha particles hit each other

5An atom has a radius of 1.0 × 10⁻¹⁰ m and its nucleus 1.0 × 10⁻¹⁵ m. Atom radius ÷ nucleus radius =

6Which idea from today is still the least clear to you?

What a good answer looks like

There is no single right answer. A good answer names one idea exactly, for example: “I am not sure why the Thomson model cannot explain the alpha particles that bounce back.”

7Feedforward: Next time I will check ________ before I ________.

What a good answer looks like

A good feedforward names an action: “Next time I will check whether a number is a radius or a volume before I compare sizes.”

TOK · 2 minutes

Theory of knowledge: how do we know? There is no single right answer. Write two or three sentences.

TOKNobody has ever seen a nucleus. Rutherford concluded that it exists from the way invisible alpha particles were scattered. How can we know about things that we can never observe directly?

Points you could make

We infer them from their effects: the scattering pattern could only be explained by a tiny, dense, positive centre.
The inference is trusted because the model makes predictions that are confirmed (for example how the counts change with angle and with the charge of the nucleus).
Our knowledge is a model, not a picture: it may be revised, as Rutherford’s atom was by Bohr and later by quantum physics.

Read the notes Part 2 Back to E.1

The nuclear atom

Learning goals: by the end you can…

1. Start with predictions

2. The gold foil: test prediction 1.1

3. Which model? Test prediction 1.2

4. Nuclear notation: test prediction 1.3

5. Sizes: test prediction 1.4

6. Show it, then reflect

Exit ticket (no notes)