22.1.2Quantum and nuclear physics (A Level)
Energy and Momentum of a Photon
5 min read 8 parts Lesson 4 of 23 1 quiz
Lesson summary
22.1.2 Energy and Momentum of a Photon — AS PHYSICS 9702 notes: Calculate the energy and momentum of a photon and use the momentum to explain the force exerted by light on a surface.Photon energy — E = hf, where E is in joules, h is the Planck constant and f is the frequency in h…
- In terms of wavelength
- Dependence
- Limit of the equation
- Momentum exists
- Momentum equation
- In terms of energy
Section 1 of 8Energy in terms of frequency and wavelength
Photon energy
- E = hf, where E is in joules, h is the Planck constant and f is the frequency in hertz.
In terms of wavelength
- Using c = fλ, the energy is E = hc/λ.
- The product hc = 1.99 × 10−25 J m is a useful value to remember.
Dependence
- Photon energy is proportional to frequency and inversely proportional to wavelength.
- A long-wavelength photon has less energy than a short-wavelength photon.
- Halving the wavelength doubles the photon energy.
Limit of the equation
- E = hf applies only to the energy of a photon, not to any other particle.
Section 2 of 8Momentum of a photon
Momentum exists
- A photon has momentum even though it has no mass.
Momentum equation
- Momentum equation p = h/λ.
In terms of energy
- Combining with E = hc/λ gives p = E/c.
- The direction of the momentum is the direction of travel.
Size
- Because c is very large, photon momenta are tiny.
Units
- For p in kg m s−1, the energy must be in joules and c in m s−1.
Section 3 of 8Force and radiation pressure
Momentum transfer
- When photons are absorbed or reflected, their momentum is transferred to the surface.
Newton's second law
- Force = rate of change of momentum, so a surface absorbing N photons per second, each of momentum p, feels F = Np.
Total absorption
- The photon momentum changes from p to 0, so F = Np = P/c for a beam of power P.
- The number of photons per second is N = P/E = P/(pc).
Perfect reflection
- At normal incidence each photon's momentum changes from p to −p, a change of 2p.
- The force doublesF = 2Np = 2P/c.
Radiation pressure
- Pressure = force ÷ illuminated area.
- The effect is measurable only with powerful beams or sensitive instruments.
Section 4 of 8Photon momentum in other processes
1Emission by an atom
- The atom recoils in the opposite direction to the emitted photon.
- The recoil speed is tiny because the atom's mass is large.
- The recoil energy p2/2M is negligible compared with the photon energy, so recoil is ignored in spectral line calculations.
2Pair production
- A gamma photon of sufficient energy becomes an electron and a positron.
- Momentum is conserved, so it occurs near a nucleus that can take up some momentum.
3Compton scattering
- A photon colliding with an electron loses energy and its wavelength increases.
- It is evidence that photons carry momentum.
4Link to matter waves
- The relation p = h/λ is the same equation as the de Broglie wavelength of a particle with mass.
Section 5 of 8Photons compared with particles with mass
| Quantity | Photon | Particle with mass |
|---|---|---|
| Energy | hf = hc/λ | ½mv2 (non-relativistic) |
| Momentum | h/λ = E/c | mv |
| Speed | always c in a vacuum | any value below c |
| Relation of E and p | E = pc | E = p2/2m |
- Distinguishing feature
- For a photon E is proportional to p, whereas for a slow particle E is proportional to p2.
Section 6 of 8More from the specification
More from the specification
Photon Energy and Discrete Quanta
- Electromagnetic radiation consists of discrete packets of energy known as photons,
- where each photon has energy given by E = hf = hc/λ, directly proportional to frequency and inversely proportional to wavelength.
The Electronvolt (eV)
- An electronvolt is defined as the kinetic energy acquired by a particle carrying elementary charge e when accelerated through a potential difference of 1 V,
- where 1 eV = 1.60 × 10⁻¹⁹ J.
Photon Momentum and Radiation Pressure
- A photon carries momentum equal to p = E/c = h/λ;
- when a monochromatic laser beam strikes an absorbing metal plate, the transfer of momentum exerts a measurable radiation pressure on the plate surface.
Photoelectric Emission and Work Function
- When photons strike a metal plate, their discrete energy is transferred to conduction electrons;
- if the photon energy exceeds the work function Φ, electrons are emitted with maximum kinetic energy KE_max = hf - Φ.
Photon Energy and Discrete Quanta
- Electromagnetic radiation consists of discrete packets of energy known as photons,
- where each photon has energy given by E = hf = hc/λ, directly proportional to frequency and inversely proportional to wavelength.
The Electronvolt (eV)
- An electronvolt is defined as the kinetic energy acquired by a particle carrying elementary charge e when accelerated through a potential difference of 1 V,
- where 1 eV = 1.60 × 10⁻¹⁹ J.
Photon Momentum and Radiation Pressure
- A photon carries momentum equal to p = E/c = h/λ;
- when a monochromatic laser beam strikes an absorbing metal plate, the transfer of momentum exerts a measurable radiation pressure on the plate surface.
Photoelectric Emission and Work Function
- When photons strike a metal plate, their discrete energy is transferred to conduction electrons;
- if the photon energy exceeds the work function Φ, electrons are emitted with maximum kinetic energy KE_max = hf - Φ.
Potential difference
- Work done by a unit charge passing through a component.
Kinetic energy
- K = ½mv2, energy of motion.
Electronvolt
- Energy gained by an electron through 1 V, 1.60 × 10⁻¹⁹ J
Charge
- Quantity of electricity in coulombs, Q = It.What the symbols mean: Q = charge (C) · I = current (A) · t = time (s)
Theory
- A well-tested, wide-ranging explanation supported by evidence.
Section 7 of 8Key terms
| Term | Meaning |
|---|---|
| Photon energy | E = hf = hc/λ, the energy carried by one photon. |
| Photon momentum | p = h/λ = E/c, the momentum carried by one photon. |
| Radiation pressure | The pressure exerted on a surface by absorbed or reflected radiation because photons transfer momentum. |
| Planck constant (h) | 6.63 × 10−34 J s, the constant linking photon energy and frequency. |
| Speed of light (c) | 3.00 × 108 m s−1 in a vacuum, the speed of every photon. |
Section 8 of 8Exam technique
1
Saying a photon has no momentum because it has no mass — a photon has momentum p = h/λ = E/c.
2
Using p = mv for a photon — use p = h/λ or p = E/c.
3
Forgetting the factor 2 for reflection — reflection gives twice the force of absorption at normal incidence.
4
Mixing up E = hc/λ and p = h/λ — the energy equation has the extra factor c.
5
Not converting nanometres to metres — wavelengths must be in metres in these equations.