Describe the path of an alpha particle that passes some distance to one side of a nucleus.

It follows a curved path that bends away from the nucleus, gradually straightening again as it recedes, so it leaves along a new straight line at some angle to its original direction.

Describe the path of an alpha particle aimed directly at a nucleus.

It slows down, momentarily stops at its distance of closest approach and then travels back out along the same line.

What happens to the kinetic energy of an alpha particle as it approaches a nucleus?

The kinetic energy falls as it is converted into electrical potential energy, because the particle is doing work against the repulsion of the nucleus.

An alpha particle of kinetic energy 5.0 MeV is fired directly at a gold nucleus. Calculate its distance of closest approach.

The kinetic energy is 5.0 × 10⁶ × 1.60 × 10⁻¹⁹ = 8.0 × 10⁻¹³ J, so r = kQq/Ek = 8.98 × 10⁹ × 1.26 × 10⁻¹⁷ × 3.20 × 10⁻¹⁹ ÷ 8.0 × 10⁻¹³ = 4.5 × 10⁻¹⁴ m.

OCR A-Level Physics B H557

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Probing Deep Into Matter

Paths of scattered particles and closest approach

3 things to know
Components 01, 02 and 03

Overview

Recall questions on paths near and straight at a nucleus, the energy exchange on approach, calculating a closest approach, why it only bounds the nuclear radius, and how scattering varies with angle.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Why does the distance of closest approach give only an upper limit for the radius of a nucleus?

Numbers

Write the relationship used to calculate the distance of closest approach for a head-on collision.

Numbers

Calculate the charge on a gold nucleus, which has 79 protons.

Questions from this subtopic

Each one with the model answer underneath.

1
Describe the path of an alpha particle that passes some distance to one side of a nucleus.
Model answer
It follows a curved path that bends away from the nucleus, gradually straightening again as it recedes, so it leaves along a new straight line at some angle to its original direction.
2
Describe the path of an alpha particle aimed directly at a nucleus.
Model answer
It slows down, momentarily stops at its distance of closest approach and then travels back out along the same line.
3
What happens to the kinetic energy of an alpha particle as it approaches a nucleus?
Model answer
The kinetic energy falls as it is converted into electrical potential energy, because the particle is doing work against the repulsion of the nucleus.
4
Write the relationship used to calculate the distance of closest approach for a head-on collision.
Model answer
All the initial kinetic energy has become electrical potential energy at that point, so Ek = kQq/r and therefore r = kQq/Ek.
5
Calculate the charge on a gold nucleus, which has 79 protons.
Model answer
The charge is 79 × 1.60 × 10⁻¹⁹ = 1.26 × 10⁻¹⁷ C.
6
An alpha particle of kinetic energy 5.0 MeV is fired directly at a gold nucleus. Calculate its distance of closest approach.
Model answer
The kinetic energy is 5.0 × 10⁶ × 1.60 × 10⁻¹⁹ = 8.0 × 10⁻¹³ J, so r = kQq/Ek = 8.98 × 10⁹ × 1.26 × 10⁻¹⁷ × 3.20 × 10⁻¹⁹ ÷ 8.0 × 10⁻¹³ = 4.5 × 10⁻¹⁴ m.

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