Photon evidence, energy and momentum
Key idea: H2 Physics lessons on photons, matter waves, wavefunctions, uncertainty and atomic spectra.
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The core idea
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Big question: What evidence forces light to be treated as packets of energy?
A photon is one quantum of electromagnetic radiation with energy E = hf and momentum p = E/c = h/λ. The photoelectric threshold shows why a packet model is needed: below the threshold frequency, even intense light cannot supply enough energy in one photon to release an electron. Interference and diffraction remain evidence for light's wave behaviour.
Connect photon energy and momentum to frequency
A photon is a quantum of electromagnetic energy E = hf = hc/λ and carries momentum p = h/λ. Higher frequency means greater energy; greater wavelength means smaller energy and momentum. Intensity changes photon arrival rate for fixed frequency, not the energy of each photon.
Photon interactions occur as whole quanta. This particle model does not erase diffraction and interference: quantum objects display wave and particle behaviour depending on the experiment.
Check your understanding: Red and violet beams have equal intensity. Which photons have greater energy?
Violet photons, because their frequency is higher. The red beam must then contain more photons per second for equal power.
Use threshold frequency as evidence
Photoelectric emission occurs only when the light frequency exceeds a threshold for the material. Below that threshold, increasing intensity sends more photons but does not increase the energy hf carried by each photon, so emission still does not occur.
This observation supports a particulate model because one electron receives energy from one photon rather than collecting small amounts continuously from the whole wave. Interference and diffraction, however, still support the wave model of electromagnetic radiation.
Check your understanding: Why can very intense light below threshold still fail to eject electrons?
It supplies more photons, but every photon still has energy hf below the amount needed for emission.
Key ideas to keep
- Below threshold, increasing intensity does not eject electrons.
- Intensity changes how many photons arrive, while frequency changes the energy of each photon.
- Photon rest mass is zero, yet photon momentum is not.
See the reasoning
Worked example
Find both energy and momentum of one photon
Question: A photon has λ = 500 nm. Find its energy and momentum.
Step 1: Convert wavelength
Why: The constants use SI units.
Working: λ = 500 nm = 5.00 × 10⁻⁷ m.
Step 2: Calculate photon energy
Why: A photon's quantum energy is fixed by frequency or wavelength.
Working: E = hc/λ = 3.98 × 10⁻¹⁹ J.
Step 3: Calculate momentum independently
Why: A photon has momentum despite zero rest mass.
Working: p = h/λ = E/c = 1.33 × 10⁻²⁷ kg m s⁻¹.
Answer: E = hc/λ = 3.98 × 10⁻¹⁹ J and p = h/λ = E/c = 1.33 × 10⁻²⁷ kg m s⁻¹. A photon is massless but has momentum.
Check: Multiplying p by c returns the calculated photon energy.
Use a hint if needed
Practise with support
Try this
Frequency doubles. State photon energy and momentum factors.
Hint: Keep intensity separate from frequency.
Check your answer
Both E = hf and p = hf/c double.
Now work without the hint
Practise independently
Your turn
Build one evidence argument distinguishing particle and wave behaviour of electromagnetic radiation, then state photon energy and momentum relations.
Check your answer
Threshold frequency supports energy transfer in photons: below threshold no photon has enough energy, regardless of intensity. Interference and diffraction support wave behaviour. E = hf, p = E/c = h/λ; zero rest mass does not mean zero momentum.
Avoid these traps
Common mistakes
Common mistake
Greater intensity raises each photon's energy.
What is wrong with this reasoning?
Show better thinking
At fixed frequency, E = hf is unchanged; intensity raises photon arrival rate.
Common mistake
A massless photon has no momentum.
What is wrong with this reasoning?
Show better thinking
Photon momentum is p = E/c = h/λ despite zero rest mass.
Write for the examiner
Exam guidance
Separate observations caused by photon energy from those caused by photon number.
Exam-style practice [6 marks]
A photon has energy 3.20 × 10⁻¹⁹ J. Find frequency and momentum, then state why threshold frequency is particle evidence.
Plan before you answer
- Use E = hf for frequency.
- Use p = E/c.
- Explain threshold with individual photon energy.
Mark your answer and compare the model
Marking points
Tick each point only if your answer states it clearly.
Model answer
f = E/h = 4.83 × 10¹⁴ Hz and p = E/c = 1.07 × 10⁻²⁷ kg m s⁻¹. A single photon below threshold cannot supply the required quantum even when more such photons arrive.
Come back in three days
Check what stayed with you
Recall question
A photon's wavelength halves. State energy and momentum factors.
Check the answer
Both double because E = hc/λ and p = h/λ.
Syllabus and review details
This lesson covers the listed H2 Physics 9478 outcomes. Use ΔxΔp ≳ h in the form given in the syllabus. Infinite-square-well results apply to a one-dimensional well with ψ zero at both infinite walls and n = 1, 2, …. Photon and matter-wave evidence supports complementary quantum descriptions. X-ray production, solving the Schrödinger equation, finite barriers, tunnelling and scanning tunnelling microscopy are not required here.
- GCE A-Level H2 PhysicsTopic 19(a) / Topic 19(b) / Topic 19(c) · 2027Checked against the syllabus · partial topic coverageOfficial 9478 syllabus
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027