What did the undeflected alpha particles show?

That most of the volume of an atom is empty space.

What did the large-angle scattering show?

That the positive charge and most of the mass of an atom are in a very small, dense nucleus.

What did the plum pudding model predict for alpha scattering?

Only small deflections, since the positive charge is spread through the atom.

What is the distance of closest approach?

The distance at which an alpha particle fired head-on is momentarily at rest and its kinetic energy has become electric potential energy.

Write the equation used to find the closest approach distance.

Ek = Qq/(4πε₀r), so r = Qq/(4πε₀Ek).

Why does closest approach give only an upper limit for nuclear radius?

The alpha particle is stopped outside the nucleus by repulsion and never touches it.

Why must electrons be of very high energy to find nuclear size?

λ = h/p, so a wavelength similar to the nuclear size (about 10⁻¹⁵ m) needs a very large momentum.

What does the intensity of electron scattering against angle look like?

A diffraction pattern: intensity falls to a first minimum then rises to a smaller maximum.

How is nuclear diameter found from the first minimum?

sin θ ≈ 1.22λ/D, so D = 1.22λ/sin θ.

State the relationship between nuclear radius and nucleon number.

R = R₀A^(1/3), where R₀ is about 1.2 fm.

What does R = R₀A^(1/3) show about nuclear density?

Volume is proportional to A and mass is proportional to A, so nuclear density is constant for all nuclei.

What is the approximate density of nuclear matter?

About 2.3 × 10¹⁷ kg m⁻³.

What is a typical nuclear radius?

Between about 1 fm and 8 fm, or around 10⁻¹⁵ m.

Rutherford scattering and nuclear radiusAQA A-Level Physics: Flashcards

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Why was the gold foil in Rutherford's experiment very thin?

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Why was the gold foil in Rutherford's experiment very thin?: So each alpha particle was scattered by only one nucleus, making the angle easy to interpret.
What did the undeflected alpha particles show?: That most of the volume of an atom is empty space.
What did the large-angle scattering show?: That the positive charge and most of the mass of an atom are in a very small, dense nucleus.
What did the plum pudding model predict for alpha scattering?: Only small deflections, since the positive charge is spread through the atom.
What is the distance of closest approach?: The distance at which an alpha particle fired head-on is momentarily at rest and its kinetic energy has become electric potential energy.
Write the equation used to find the closest approach distance.: Ek = Qq/(4πε₀r), so r = Qq/(4πε₀Ek).
Why does closest approach give only an upper limit for nuclear radius?: The alpha particle is stopped outside the nucleus by repulsion and never touches it.
Why must electrons be of very high energy to find nuclear size?: λ = h/p, so a wavelength similar to the nuclear size (about 10⁻¹⁵ m) needs a very large momentum.
What does the intensity of electron scattering against angle look like?: A diffraction pattern: intensity falls to a first minimum then rises to a smaller maximum.
How is nuclear diameter found from the first minimum?: sin θ ≈ 1.22λ/D, so D = 1.22λ/sin θ.
State the relationship between nuclear radius and nucleon number.: R = R₀A^(1/3), where R₀ is about 1.2 fm.
What does R = R₀A^(1/3) show about nuclear density?: Volume is proportional to A and mass is proportional to A, so nuclear density is constant for all nuclei.
What is the approximate density of nuclear matter?: About 2.3 × 10¹⁷ kg m⁻³.
What is a typical nuclear radius?: Between about 1 fm and 8 fm, or around 10⁻¹⁵ m.

Exam questions on Rutherford scattering and nuclear radius

In an alpha particle scattering experiment, a narrow beam of alpha particles from a radioactive source is fired at a thin gold foil inside an evacuated chamber. A detector counts the alpha particles scattered through different angles. Almost all the particles pass through the foil, but about 1 in 8000 is scattered through an angle greater than 90°.
The gold foil used is only a few hundred atoms thick. Explain why a much thicker foil would make the results difficult to interpret.2 marks
An alpha particle of kinetic energy 7.7 MeV is fired directly towards the centre of a stationary gold nucleus, which has proton number 79. The alpha particle is brought momentarily to rest at a distance r from the centre of the nucleus before it is repelled. The gold nucleus can be assumed to remain at rest.
The distance of closest approach for this alpha particle is 3.0 × 10⁻¹⁴ m. Explain why this gives only an upper limit for the radius of the gold nucleus.2 marks
A beam of electrons of kinetic energy 420 MeV is directed at a thin target of carbon-12 nuclei. The scattered electrons are detected at different angles and the intensity shows a diffraction pattern, with the first minimum at 40° to the original direction. For these electrons, use E = pc. The first minimum occurs when sin θ = 1.22λ/D, where λ is the electron wavelength and D is the diameter of the nucleus.
Calculate the wavelength of the electrons.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).