AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Students should be familiar with the graph of intensity against angle for…
Full specification wording
Nuclear radius (A-level only): Students should be familiar with the graph of intensity against angle for electron diffraction by a nucleus.
When electrons are accelerated through a potential difference and directed at a thin nuclear target, they diffract.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 6 of 6
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
When electrons are accelerated through a potential difference and directed at a thin nuclear target, they diffract. A graph of intensity against angle shows a central maximum at zero angle and a series of minima and weaker maxima at increasing angles. The first minimum occurs at an angle θ where sin θ ≈ λ/D, with D the nuclear diameter and λ the de Broglie wavelength of the electrons. Increasing electron energy decreases λ, so the pattern narrows and the first minimum moves to a smaller angle. The graph therefore provides evidence for a nuclear radius of the order of 10⁻¹⁵ m and supports the model of the nucleus as a small, dense, roughly spherical object.
What earns the marks
- Describes the shape of the graph: a large central maximum at zero angle, followed by minima and smaller secondary maxima at larger angles.
- Identifies that the first minimum occurs at an angle related to the nuclear diameter by sin θ ≈ λ/D, where λ is the electron de Broglie wavelength.
- Explains that higher electron energy gives a shorter de Broglie wavelength and therefore a narrower diffraction pattern with the first minimum at a smaller angle.
- Uses the position of the first minimum to estimate the nuclear diameter or radius, giving values of the order of 10⁻¹⁵ m.
- Recognises that the diffraction pattern is evidence for the wave nature of electrons and for the small size of the nucleus.
Common mistakes and how to put them right
Confusing the angle of the first minimum with the angle of the first maximum.
Put it right: Identify the first minimum as the first point of zero intensity after the central peak.
Assuming the pattern broadens as electron energy increases.
Put it right: Higher energy means shorter wavelength and a narrower pattern.
Using the wavelength of visible light instead of the electron de Broglie wavelength.
Put it right: Calculate λ = h/p from the accelerated electron momentum.
Exam tips
- Sketch the graph with intensity on the vertical axis and angle on the horizontal axis, labelling the central maximum and first minimum clearly.
- Quote the relationship sin θ ≈ λ/D when explaining how the graph is used to estimate nuclear size.
- Link changes in electron energy to changes in wavelength and then to changes in the angular width of the pattern.
Try the lesson
The start of the Nuclear radius (A-level only): Students should be familiar with the graph of intensity against angle for electron diffraction by a nucleus. lesson, made from checked teaching notes for this specification point.
Have a go first
In an electron diffraction experiment, a graph of intensity against angle is plotted. What does the angle of the first minimum in this graph indicate about the nucleus?
Listen
When electrons are accelerated through a potential difference and directed at a thin nuclear target, they diffract. A graph of intensity against angle shows a central maximum at zero angle and a series of minima and weaker maxima at increasing angles. The first minimum occurs at an angle θ where sin θ ≈ λ/D, with D the nuclear diameter and λ the de Broglie wavelength of the electrons. Increasing electron energy decreases λ, so the pattern narrows and the first minimum moves to a smaller angle. The graph therefore provides evidence for a nuclear radius of the order of 10⁻¹⁵ m and supports the model of the nucleus as a small, dense, roughly spherical object. A strong answer earns marks for these points. Describes the shape of the graph: a large central maximum at zero angle, followed by minima and smaller secondary maxima at larger angles. Identifies that the first minimum occurs at an angle related to the nuclear diameter by sin θ ≈ λ/D, where λ is the electron de Broglie wavelength. Explains that higher electron energy gives a shorter de Broglie wavelength and therefore a narrower diffraction pattern with the first minimum at a smaller angle. Uses the position of the first minimum to estimate the nuclear diameter or radius, giving values of the order of 10⁻¹⁵ m. A common slip: Confusing the angle of the first minimum with the angle of the first maximum. Instead, identify the first minimum as the first point of zero intensity after the central peak. Exam tip: Sketch the graph with intensity on the vertical axis and angle on the horizontal axis, labelling the central maximum and first minimum clearly.
Key words
Say what each word means before you turn the card.
Intensity–angle graph
Try answering aloud or in your head before turning the card.
First minimum
Try answering aloud or in your head before turning the card.
de Broglie wavelength
Try answering aloud or in your head before turning the card.
Nuclear radius
Try answering aloud or in your head before turning the card.
See every definition
- Intensity–angle graph
- A graph showing a central maximum at zero angle and a series of minima and weaker maxima at increasing angles.
- First minimum
- Occurs at an angle θ where sin θ ≈ λ/D, with D the nuclear diameter and λ the de Broglie wavelength of the electrons.
- de Broglie wavelength
- Increasing electron energy decreases it, so the pattern narrows and the first minimum moves to a smaller angle.
- Nuclear radius
- The graph provides evidence for a value of the order of 10⁻¹⁵ m and supports the model of the nucleus as a small, dense, roughly spherical object.
There is more to this lesson
The full lesson goes on to check your understanding and help you earn the marks. Create a free account to carry on, with your progress saved.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge
Test your understanding of Nuclear radius (A-level only): Students should be familiar with the graph of intensity against angle for electron diffraction by a nucleus.
Active recall beats re-reading. Take an instant quiz now to test what you’ve learned and lock it into long-term memory.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge