All equation deep-dives

Photon energy and de Broglie wavelength

Particles and radiation
AQA 7408
In the data booklet
ORIGINAL

E = h f and lambda = h / p

Derived · not in booklet
E = h c / lambdaDerived from the given E = h f and c = f lambda; it is not printed verbatim.
Derived · not in booklet
lambda = h c / EA rearrangement of the derived E = h c / lambda form.

Nanometres and electronvolts are the traps: convert to metres and joules before using the booklet equations.

Verified against AQA 7408 (2026 spec)

Know the equation

SymbolQuantityUnit
Ephoton energyJ
hPlanck constantJ s
fphoton frequencyHz
cspeed of light in vacuumm/s
lambdawavelengthm
pparticle momentumkg m/s
mparticle masskg
vparticle speedm/s

Rearrangements

  • f = E / h
  • p = h / lambda
  • lambda = h / (m v)

Apply it — mark your own working

Work each one out on paper first, then reveal the mark scheme and tick the marks you actually earned. That is exactly how you should mark past papers.

Q1
4 marks

Calculate the energy of a photon of wavelength 450 nm in joules and electronvolts. Use h = 6.63 x 10−34 J s, c = 3.00 x 108 m/s and 1 eV = 1.60 x 10−19 J.

Do the calculation on paper first — then mark it.

Q2
3 marks

An electron of mass 9.11 x 10−31 kg moves at 2.5 x 106 m/s. Calculate its de Broglie wavelength. Use h = 6.63 x 10−34 J s.

Do the calculation on paper first — then mark it.

Where the marks get lost

  • Using wavelength in nanometres without multiplying by 10−9.
  • Converting joules to electronvolts in the wrong direction; divide the joule value by 1.60 x 10−19.
  • Using lambda = h/m and forgetting the velocity in momentum p = m v.

Exam tip: Write the momentum step explicitly before using lambda = h/p. It earns the method clearly and prevents a missing mass or speed factor.

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