Energy of a Photon
Energy of a photon from its frequency.
Formula
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Example
A photon of green light (~5.5×10¹⁴ Hz) carries E = h·f ≈ 3.6×10⁻¹⁹ J.
How it works
Light does not exchange energy in a continuous trickle; at the microscopic level it comes in packets called photons. The size of each packet is proportional to the wave’s frequency, so higher-frequency radiation carries more energy per photon, with Planck’s constant h acting as the conversion factor between frequency and energy. This relationship comes from quantum theory and explains why ultraviolet light can trigger effects that visible or infrared light cannot, even if the beam looks equally bright.
When to use it
Use this formula whenever you need the energy of a single photon from a known frequency, such as in spectroscopy, photoelectric-effect problems, or comparing different parts of the electromagnetic spectrum. It is also useful for finding wavelength-based photon energies after converting wavelength to frequency.
Worked example, step by step
A radio transmitter emits photons at a frequency of 1.20 × 10^8 Hz. Step 1: Write the formula: E = hf Step 2: Substitute the values: E = (6.626 × 10^-34 J·s)(1.20 × 10^8 s^-1) Step 3: Multiply the numbers: E = 7.95 × 10^-26 J Step 4: State the result: each photon has an energy of 7.95 × 10^-26 joules.
Common mistakes to avoid
- Using the speed of light c instead of Planck constant h
- Forgetting to convert frequency into hertz before calculating
- Calculating the energy of a whole beam of light instead of a single photon
Did You Know?
Einstein won his Nobel Prize not for relativity but for explaining that light energy comes in these discrete photon packets.
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