Photons
Light arrives in packets.
Lesson at a glanceShow the key points
- Photons travel at c and have zero rest mass.
- E = hν = hc/λ, p = h/λ = E/c (42.1); hc ≈ 1240 eV nm.
- Intensity sets photon number; wavelength sets photon energy.
- Absorbed light pushes with force P/c.
Light makes interference fringes, so it is a wave. Yet it also knocks electrons out of metals one at a time, so it comes in particles. Depending on the experiment, one face or the other shows.
The photon
Interference needs waves; the photoelectric effect (next lesson) can only be understood with particles. These particles of light are photons. Their properties:
- A photon always travels at c = 299 792 458 m/s ≈ 3.0 × 10⁸ m/s in vacuum, in every frame of reference.
- Its rest mass is zero (Newtonian mass isn’t meaningful for it).
- Each photon has a definite energy and a definite momentum, tied to the frequency and wavelength the same light shows as a wave:
- In a collision with a particle, total energy and momentum are conserved; photons can be absorbed or created, so their number need not be conserved.
- Brighter light of the same wavelength means more photons per second, not more energetic ones.
For a given wavelength, light energy can change only in whole steps of hc/λ. That is why photon theory is also called the quantum theory of light.
A parallel beam of 500 nm light has intensity 50 W/m². Find each photon’s energy and momentum, and how many cross 1 cm² each second.
How many photons does a 3.0 mW green laser (532 nm) emit each second?
A 100 W monochromatic source emits 3.0 × 10²⁰ photons per second. Find its wavelength.
Photons push
A hydrogen atom (1.67 × 10⁻²⁷ kg) absorbs a 103 nm photon coming head-on and stops dead. How fast was it moving?
A 5.0 W beam of 600 nm light falls normally on a perfectly absorbing surface. Find the photons absorbed per second and the force on the surface.
- 1Light comes in photons: speed c, zero rest mass.
- 2E = hν = hc/λ, p = h/λ = E/c (42.1); hc ≈ 1240 eV nm.
- 3Intensity sets the number of photons; wavelength sets each photon's energy.
- 4Photons carry momentum: absorbed light pushes with force P/c.
Check yourself
Keep exploring
Hand-picked videos, simulations and readings that explain this idea from a different angle.