Particle nature of light: the photon
Light is made of photons, each with energy E = hν and momentum p = h/λ. Brighter light means more photons, not stronger ones.
Properties of photons
- When radiation interacts with matter, it behaves as if it is made of particles called photons.
- Each photon has energy E = hν and momentum p = hν/c = h/λ. In vacuum, it moves at the speed of light c.
- All photons of one frequency have the same energy and momentum, whatever the intensity. Brighter light only means more photons crossing an area each second.
- Photons are electrically neutral, so electric and magnetic fields do not deflect them.
- In a collision between a photon and a particle such as an electron, total energy and total momentum are conserved.
- The number of photons need not be conserved: a photon may be absorbed, or a new photon may be created.
A quick way to find photon energy
Using h = 6.63 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s and 1 eV = 1.6 × 10⁻¹⁹ J, hc comes to about 1240 eV nm. So E (in eV) ≈ 1240 ÷ λ (in nm). This shortcut is not in your textbook, so use it to check and show the full working with h and c in the exam. Violet light of 400 nm has photons of about 3.1 eV. Red light of 700 nm has photons of about 1.8 eV. Suppose a metal has a work function of 2.75 eV. Violet light can free electrons from it, but red light cannot, however bright it is.
Worked example: energy and momentum of a photon
Find the energy (in J and eV) and the momentum of a photon of red light of wavelength 663 nm. (h = 6.63 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s)
- E = hc/λ = (6.63 × 10⁻³⁴ J s × 3 × 10⁸ m/s) ÷ (6.63 × 10⁻⁷ m).
- E = 3 × 10⁻¹⁹ J.
- In eV: 3 × 10⁻¹⁹ ÷ 1.6 × 10⁻¹⁹ = 1.875 ≈ 1.88 eV.
- p = h/λ = (6.63 × 10⁻³⁴ J s) ÷ (6.63 × 10⁻⁷ m) = 1 × 10⁻²⁷ kg m/s.
E = 3 × 10⁻¹⁹ J ≈ 1.88 eV; p = 1 × 10⁻²⁷ kg m/s
Worked example: photons from a laser pointer
A laser pointer of power 3 mW gives light of wavelength 663 nm. How many photons does it emit each second?
- Energy of one photon: E = 3 × 10⁻¹⁹ J (from the last example).
- Energy given out each second = power P = 3 × 10⁻³ J/s.
- N = P/E = (3 × 10⁻³ J/s) ÷ (3 × 10⁻¹⁹ J) = 1 × 10¹⁶ photons per second.
1 × 10¹⁶ photons per second
Brighter light vs higher-frequency light
Ultraviolet photons carry more energy than visible ones, enough to damage skin cells. That is why shade and sunscreen matter in an Indian summer, while bright red light, however strong, does not cause sunburn.
2 marks: “State any two properties of photons.” Any two: energy hν and momentum h/λ; all photons of one frequency have the same energy, and intensity changes only their number; neutral, so not deflected by fields; energy and momentum conserved in collisions.
3 marks: “A lamp gives out 6.63 W of light of wavelength 600 nm. Find the energy of each photon and the number of photons emitted per second. (h = 6.63 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s)” E = hc/λ = (6.63 × 10⁻³⁴ × 3 × 10⁸) ÷ (6 × 10⁻⁷) = 3.315 × 10⁻¹⁹ J; N = P/E = 6.63 ÷ (3.315 × 10⁻¹⁹) = 2 × 10¹⁹ photons per second.
1 marks: “How does the momentum of a photon change if its wavelength is doubled?” p = h/λ, so the momentum is halved.
E = hν, p = h/λ. Brighter means more photons; bluer means stronger photons.