Photon Energy and Momentum
For a photon in vacuum, energy is proportional to frequency and momentum is energy divided by c. Frequency and wavelength obey c = nu lambda, so shorter-wavelength photons have larger energy and momentum.
Why this shows up in the exam
Comparing photon energies across the electromagnetic spectrum · Calculating atomic absorption or emission energy · Relating light momentum to mechanical effects
Learn the idea
A photon carries discrete energy and momentum even though its rest mass is zero. Light exchanges energy in packets. A higher-frequency packet carries more energy, and every photon also carries momentum, so light can push matter without having rest mass.
🧠 Memory hook: Shorter wave, bigger photon energy and momentum.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- E = h nu = h c / lambda — energy of one photon of frequency nu and vacuum wavelength lambda
- p = E/c = h/lambda — magnitude of photon momentum in vacuum
How to approach it
- 1Identify whether the object is a photon or a massive particle
- 2Convert wavelength to metres or use a consistent h c unit
- 3Use E = h nu and p = E/c before comparing quantities
Common slip-ups that cost marks
- •Setting photon momentum to zero because photon rest mass is zero
- •Using E = pc for a massive non-relativistic particle
- •Mixing wavelength units when using h c / lambda
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Photons of energy 5 eV illuminate a metal of work function 2 eV. Find the stopping potential.
More from Dual Nature of Matter and Radiation
Photoelectric Effect
The photoelectric effect describes the emission of electrons from a material when it is exposed to light of sufficient frequency, governed by concepts such as threshold frequency, work function, stopping potential, and the Einstein photoelectric equation.
de Broglie Wavelength and Matter Waves
All matter exhibits wave-like properties, with the de Broglie wavelength inversely proportional to momentum and dependent on factors like velocity, temperature, and particle type.
Photon Properties and Energy-Momentum Relations
Photons are massless particles of light characterized by their energy, frequency, momentum, and charge neutrality, and their interactions obey conservation laws.
Photon Rate, Power, and Energy Density
For monochromatic radiation, total energy is the number of photons times h nu. Power is energy per unit time, so the photon emission rate equals power divided by single-photon energy.
Radiation Pressure and Photon Momentum Transfer
Radiation force is the rate of photon momentum transfer. For normal incidence on an ideal absorber the pressure is intensity divided by c; for an ideal reflector it is twice that value.
Photoelectric Effect Observations
For a fixed emitter, emission occurs only when incident frequency reaches the threshold frequency. Above threshold, maximum kinetic energy depends on frequency, while saturation current is primarily proportional to intensity.