Use electronvolts and calculate photon momentum
Convert between joules and electronvolts and calculate photon momentum from p = E/c.
Section 22 · Quantum physics
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 22. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use wave frequency and wavelength, energy, momentum, SI prefixes, electronvolts and scientific notation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How many joules are in 1 eV?
What you will learn
- Use the electronvolt as a unit of energy
- Convert electronvolts to joules and joules to electronvolts
- Use p = E/c to calculate photon momentum
An electronvolt is a small energy unit
One electronvolt (1 eV) is the energy transferred when an electron moves through a potential difference of 1 V. Since 1 eV = e joules, use 1 eV = 1.60 × 10⁻¹⁹ J. Convert to joules before combining energy with quantities expressed in SI units.
To convert eV to joules, multiply by 1.60 × 10⁻¹⁹; to convert joules to eV, divide by that value. Electronvolts are a unit of energy, not charge or voltage. State clearly which unit the final answer uses.
A photon has momentum even though it has no rest mass
A photon carries momentum. Its momentum magnitude is p = E/c, where E is photon energy in joules and c = 3.00 × 10⁸ m s⁻¹. The resulting unit is kg m s⁻¹. With E = hf, this can also be written p = hf/c.
Do not set photon momentum to zero by using the photon's zero rest mass: p = E/c describes its momentum from energy. If energy is supplied in eV, convert to joules before calculating p. A higher-energy photon has proportionally greater momentum.
Pause and explain
A photon has energy E in joules. Which relation gives its momentum magnitude?
Worked example
A photon has energy 2.0 eV. Find its energy in joules and momentum. Use c = 3.00 × 10⁸ m s⁻¹.
Show the worked solution
- Convert eV to joules.
- Use p = E/c with the energy in joules.
- Give momentum in kg m s⁻¹.
Answer E = 2.0 × 1.60 × 10⁻¹⁹ = 3.2 × 10⁻¹⁹ J; p = 3.2 × 10⁻¹⁹/(3.00 × 10⁸) = 1.07 × 10⁻²⁷ kg m s⁻¹.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Convert 3.5 eV to joules.
Give me a hint
Multiply the eV value by 1.60 × 10⁻¹⁹ J per eV.
Compare my reasoning
- E = 3.5 × 1.60 × 10⁻¹⁹ J.
- E = 5.60 × 10⁻¹⁹ J.
- Keep the energy unit as joules.
3.5 eV = 5.60 × 10⁻¹⁹ J.
Look for these in your work
- Conversion factor used
- Product calculated
- Joule unit stated
A photon has energy 4.8 × 10⁻¹⁹ J. Calculate its momentum.
Give me a hint
Use p = E/c with c = 3.00 × 10⁸ m s⁻¹.
Compare my reasoning
- p = E/c.
- p = 4.8 × 10⁻¹⁹/(3.00 × 10⁸).
- p = 1.6 × 10⁻²⁷ kg m s⁻¹.
p = 1.6 × 10⁻²⁷ kg m s⁻¹.
Look for these in your work
- Photon momentum relation used
- Division by c performed
- SI unit stated
Photon A has energy 1.5 eV and photon B has energy 3.0 eV. Compare their momentum magnitudes.
Give me a hint
Convert or use the proportionality p = E/c; c is common.
Compare my reasoning
- Momentum is directly proportional to photon energy.
- Photon B has twice the energy of photon A.
- Photon B therefore has twice the momentum magnitude.
Photon B has twice the momentum magnitude of photon A.
Look for these in your work
- Correct proportionality stated
- Energy ratio identified
- Momentum ratio concluded
Common mistakes
- Treating 1 eV as 1.60 × 10⁻¹⁹ C
- Dividing eV directly by c while reporting SI momentum
- Assuming photons have no momentum because their rest mass is zero
- Using c in km s⁻¹ while energy is in joules
What can you explain now?
How many joules are in 1 eV?
Compare with the explanation
1.60 × 10⁻¹⁹ J
The electronvolt is the energy transferred per elementary charge through 1 V.
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Make it stick
Why must an eV value be converted to joules before using p = E/c in SI units?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.