Photon Energy Calculation
The Intuition First
Imagine you're holding a rope tied to a wall. If you flick your wrist once, a single pulse travels down the rope. If you flick faster — more frequently — each pulse carries more energy; the rope vibrates more violently. Light behaves the same way. A photon is the smallest possible "flick" of the electromagnetic field — a single, indivisible packet of light energy.
What determines how much energy that one photon carries? Two things: how fast the wave is oscillating (its frequency), and a universal constant that connects the wave world to the particle world.
The Precise Statement
The energy E of a single photon is directly proportional to its frequency f (or inversely proportional to its wavelength λ). The proportionality constant is Planck's constant h, one of the most fundamental numbers in physics.
E=hf=λhc
Where:
- E = energy of one photon (in joules, J)
- h = Planck's constant = 6.626×10−34 J⋅s
- f = frequency of the electromagnetic wave (in hertz, Hz)
- c = speed of light = 3.00×108 m/s
- λ = wavelength of the light (in metres, m)
Why Two Forms?
The first form E=hf is the most direct: higher frequency means higher energy. The second form E=hc/λ is often more practical because wavelength is easier to measure than frequency. Since c=fλ, you can always swap between them.
What This Tells You
- Blue light (short wavelength, high frequency) has more energy per photon than red light (long wavelength, low frequency).
- Gamma rays have enormous photon energies; radio waves have tiny photon energies.
- The energy is quantised — you cannot have half a photon. Either the full energy hf is absorbed/emitted, or none at all.
A Worked Example
Question: Calculate the energy of a single photon of violet light with wavelength 400 nm.
Step 1: Convert wavelength to metres.
400 nm=400×10−9 m=4.00×10−7 m
Step 2: Use E=hc/λ.
E=4.00×10−7(6.626×10−34)(3.00×108)
Step 3: Compute.
E=4.00×10−71.9878×10−25=4.97×10−19 J
This is an incredibly tiny amount of energy — about 5×10−19 joules. That's why we often use electronvolts (eV) for photon energies in atomic physics. 1 eV=1.602×10−19 J, so this photon has about 3.1 eV.
Common Mistake to Avoid …