Photon Energy Calculation
The Core Idea
Light is not a smooth, continuous flow of energy — it comes in tiny indivisible packets called photons. Each photon carries a fixed amount of energy that depends only on the light's frequency (its colour), not on how bright the beam is. A brighter beam simply contains more photons; each individual photon still carries the same energy.
The Master Formula
E=hf=λhc
where
- E = energy of one photon (joule, J),
- h=6.63×10−34 J s is Planck's constant,
- f = frequency of the light (hertz, Hz),
- c=3×108 m/s is the speed of light, and
- λ = wavelength (metre, m).
The two forms are connected by the wave relation c=fλ. Use E=hf when you are given the frequency and E=hc/λ when you are given the wavelength.
Because E=hc/λ, energy is inversely proportional to wavelength: short-wavelength radiation (X-rays, UV) has high-energy photons; long-wavelength radiation (radio, microwave) has low-energy photons.
Working in Electron-Volts
Photon energies are tiny in joules, so we often use the electron-volt:
1 eV=1.6×10−19 J
A handy shortcut for visible/UV light expresses the energy directly from the wavelength in nanometres:
E(eV)≈λ (nm)1240
(The number 1240 is just hc expressed in eV·nm.)
Worked Example 1 — from frequency
Find the energy of a photon of frequency f=5.0×1014 Hz (green light).
E=hf=(6.63×10−34)(5.5×1014)=3.6×10−19 J
Converting to eV:
E=1.6×10−193.3×10−19≈2.1 eV
Worked Example 2 — from wavelength
Find the energy of a photon of wavelength λ=620 nm (red light).
E=λhc=620×10−9(6.63×10−34)(3×108)=3.2×10−19 J≈2.0 eV
Or with the shortcut: E≈1240/620=2.0 eV — same answer, much faster.
Total Energy of a Beam
A single photon's energy is tiny, but a real beam contains enormous numbers of them. If a source emits N photons per second (or a pulse contains N photons), the total energy is simply
Etotal=N×hf
So the number of photons carrying a given power P is …