AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Bertozzi’s experiment as direct evidence for the variation of kinetic…
Full specification wording
Mass and energy (A-level only): Bertozzi’s experiment as direct evidence for the variation of kinetic energy with speed.
Bertozzi accelerated electrons along a linear tube and timed their travel over a measured distance, giving their speed directly.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 8 of 8
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Bertozzi accelerated electrons along a linear tube and timed their travel over a measured distance, giving their speed directly. Crucially, he measured the kinetic energy delivered by the electrons independently using calorimetry, by recording the temperature rise of an aluminium target they struck. Plotting kinetic energy against speed showed that at low speeds, energy rose as ½mv². However, as v approached c, the energy increased steeply while the speed levelled off below c. This provides direct evidence that kinetic energy does not follow the classical formula at relativistic speeds and that no massive particle reaches the speed of light. The relativistic expression Eₖ = (γ − 1)mc² fits the experimental data perfectly.
What earns the marks
- Describes the method for speed: electrons are accelerated through a known potential difference and their flight time over a measured distance gives speed.
- Explains that kinetic energy is determined independently using calorimetry, by measuring the temperature rise of a target struck by the electrons.
- States the key result: measured speed approaches but never reaches c, while kinetic energy continues to rise without limit.
- Uses Eₖ = (γ − 1)mc² to show that the classical ½mv² result fails when v is a significant fraction of c.
- Explains that the experiment supports special relativity rather than classical mechanics because the classical prediction diverges from the data at high speed.
- Recognises that the result implies a limiting speed c for massive particles and links this to the relativistic increase of energy.
Common mistakes and how to put them right
Claiming Bertozzi measured kinetic energy solely from the accelerating voltage.
Put it right: He used calorimetry (target temperature rise) to measure kinetic energy independently.
Stating that electrons exceeded the speed of light at the highest energies.
Put it right: Measured speeds approached c asymptotically and never surpassed it.
Using Eₖ = ½mv² for the high-speed data.
Put it right: Use the relativistic expression Eₖ = (γ − 1)mc² when v is comparable to c.
Exam tips
- Describe the independent measurements of speed (time of flight) and kinetic energy (calorimetry) separately, because the strength of the evidence depends on them being measured by different means.
- Sketch or interpret the graph shape: classical ½mv² rising as a parabola against the relativistic curve that steepens near c.
- Use the phrase direct evidence and explain what would be expected classically, so the contrast with the data is explicit.
- Quote the limiting behaviour of speed near c rather than saying electrons were stopped or slowed.
Try the lesson
The start of the Mass and energy (A-level only): Bertozzi’s experiment as direct evidence for the variation of kinetic energy with speed. lesson, made from checked teaching notes for this specification point.
Have a go first
In Bertozzi's experiment, electrons were accelerated through a measured potential difference and their time of flight over a fixed distance was recorded. What did the results show about the electrons as their speed approached the speed of light?
Listen
Bertozzi accelerated electrons along a linear tube and timed their travel over a measured distance, giving their speed directly. Crucially, he measured the kinetic energy delivered by the electrons independently using calorimetry, by recording the temperature rise of an aluminium target they struck. Plotting kinetic energy against speed showed that at low speeds, energy rose as ½mv². However, as v approached c, the energy increased steeply while the speed levelled off below c. This provides direct evidence that kinetic energy does not follow the classical formula at relativistic speeds and that no massive particle reaches the speed of light. The relativistic expression Eₖ = (γ − 1)mc² fits the experimental data perfectly. A strong answer earns marks for these points. Describes the method for speed: electrons are accelerated through a known potential difference and their flight time over a measured distance gives speed. Explains that kinetic energy is determined independently using calorimetry, by measuring the temperature rise of a target struck by the electrons. States the key result: measured speed approaches but never reaches c, while kinetic energy continues to rise without limit. Uses Eₖ = (γ − 1)mc² to show that the classical ½mv² result fails when v is a significant fraction of c. A common slip: Claiming Bertozzi measured kinetic energy solely from the accelerating voltage: the error misses the independent verification. Instead, he used calorimetry (target temperature rise) to measure kinetic energy independently. Exam tip: Describe the independent measurements of speed (time of flight) and kinetic energy (calorimetry) separately, because the strength of the evidence depends on them being measured by different means.
Key words
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Limiting speed c for massive particles
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Breakdown of classical mechanics at relativistic speeds
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Relativistic kinetic energy and the Lorentz factor
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See every definition
- Limiting speed c for massive particles
- As v approached c the speed levelled off below c, so no massive particle reaches the speed of light.
- Breakdown of classical mechanics at relativistic speeds
- Kinetic energy does not follow the classical formula at relativistic speeds, and the classical prediction diverges from the data at high speed.
- Relativistic kinetic energy and the Lorentz factor
- The relativistic expression Eₖ = (γ − 1)mc² fits the experimental data perfectly, while energy increased steeply as v approached c.
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