Photons and energy: E = hf
Light and all EM waves travel as tiny packets of energy called photons. One photon carries energy E = hf, where h = 6.63 × 10⁻³⁴ J s (Planck's constant) and f is the frequency. Using c = fλ, we can also write E = hc/λ.
So short wavelength = high frequency = high photon energy. A gamma photon carries millions of times more energy than a radio photon.
Small energies are often given in electronvolts: 1 eV = 1.6 × 10⁻¹⁹ J. Visible photons carry about 2–3 eV.
What each part of the spectrum does to matter
When radiation meets matter it can be reflected, transmitted (passes through) or absorbed. What happens depends on photon energy and the material.
- Radio: passes through walls and bodies; makes tiny currents in metal aerials.
- Microwave: absorbed by water; makes molecules rotate → heating. Used in ovens and mobile phones (at very low power).
- Infrared: makes molecules vibrate → warming. We feel it as heat from the Sun or a stove.
- Visible: lifts electrons to higher levels. Absorbed colours vanish, reflected colours are seen. Drives photosynthesis and vision.
- Ultraviolet: enough energy to break some chemical bonds → sunburn, skin ageing, DNA damage; also makes vitamin D and kills germs.
- X-rays: pass through soft tissue, absorbed more by bone → X-ray images. Ionising.
- Gamma: highest energy, very penetrating, strongly ionising. Used to kill cancer cells and sterilise equipment.
Ionising and non-ionising radiation
To knock an electron out of a typical atom needs roughly 10 eV or more. Photons with this much energy are ionising: high UV, X-rays and gamma rays. Ions are very reactive and can break DNA, which may lead to mutations or cancer.
Radio, microwave, infrared and visible light are non-ionising. Their main effect on the body is heating. A brighter (more intense) beam has more photons, not stronger photons, so even a very bright radio wave cannot ionise; it can only heat.
Risk and safety
The harm from radiation depends on: photon energy (type), intensity (how many photons per second per area) and time of exposure. Distance helps too: intensity falls quickly as you move away.
Safety examples: lead aprons and short exposures for X-rays; sunscreen, hats and shade for UV; safety limits on the power of phone and Wi-Fi transmitters. When you read a claim about radiation, ask: what type, how intense, how long, and what does good evidence say?
Try it
Put a black cloth and a white cloth in the sun for 10 minutes and touch them. The black one absorbed more visible and infrared radiation, so it is warmer. In the 3D, slide the band and note E for radio, visible and gamma. How many times bigger is gamma than visible?
Key formulas and definitions
- E = hf
- E = hc / λ
- c = fλ, c = 3 × 10⁸ m/s
- h = 6.63 × 10⁻³⁴ J s
- 1 eV = 1.6 × 10⁻¹⁹ J
- Intensity = power / area
Worked examples
1. Find the energy of a photon of frequency 5 × 10¹⁴ Hz.
E = hf = 6.63 × 10⁻³⁴ × 5 × 10¹⁴ = 3.3 × 10⁻¹⁹ J.
2. Convert 3.3 × 10⁻¹⁹ J to eV.
E = 3.3 × 10⁻¹⁹ ÷ 1.6 × 10⁻¹⁹ ≈ 2.1 eV (visible light).
3. Find the frequency of microwaves of wavelength 12 cm.
f = c/λ = 3 × 10⁸ ÷ 0.12 = 2.5 × 10⁹ Hz (2.5 GHz).
4. Find the energy of a UV photon of wavelength 200 nm in eV. Is it ionising?
E = hc/λ = 6.63 × 10⁻³⁴ × 3 × 10⁸ ÷ 2 × 10⁻⁷ = 9.9 × 10⁻¹⁹ J ≈ 6.2 eV. It is below about 10 eV, so it does not ionise most atoms, but it can break chemical bonds.
5. An X-ray photon has λ = 0.1 nm. How many times more energy does it have than a 500 nm visible photon?
E ∝ 1/λ, so ratio = 500 ÷ 0.1 = 5000 times.
6. A 1000 W microwave oven gives out photons of 2.45 GHz. How many photons per second?
Energy per photon = hf = 6.63 × 10⁻³⁴ × 2.45 × 10⁹ = 1.62 × 10⁻²⁴ J. Number = 1000 ÷ 1.62 × 10⁻²⁴ ≈ 6.2 × 10²⁶ photons per second. Huge numbers, but each is too weak to ionise.
Common mistakes
- Thinking a brighter (more intense) beam has higher-energy photons. Intensity changes the number of photons, not the energy of each one.
- Calling all "radiation" dangerous. Radio, microwave, infrared and visible are non-ionising.
- Forgetting to convert nm to m (1 nm = 10⁻⁹ m) in E = hc/λ.
- Thinking microwaved food becomes radioactive. Microwaves only heat; they cannot make atoms radioactive.