Photon Energy
Energy of a single photon.
Formula
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How it works
A photon is a single packet of electromagnetic radiation, and its energy is directly proportional to the wave’s frequency. Planck’s constant, h, sets the size of the energy step for each cycle of oscillation, so higher-frequency light such as ultraviolet or X-rays carries more energy per photon than lower-frequency light such as radio waves. This relationship comes from quantum theory, where light is not just a continuous wave but is emitted and absorbed in discrete amounts.
When to use it
Use this formula whenever you need the energy of one photon from a known frequency, or when comparing how energetic different parts of the electromagnetic spectrum are. It is especially useful in photoelectric effect questions, spectroscopy, laser physics, and radiation safety.
Worked example, step by step
Find the energy of a photon of green light with frequency 5.50 × 10^14 Hz. Use E = hf Substitute the values: E = (6.626 × 10^-34 J·s)(5.50 × 10^14 s^-1) Multiply the numbers: 6.626 × 5.50 = 36.443 Combine powers of ten: 10^-34 × 10^14 = 10^-20 So E = 36.443 × 10^-20 J Write in standard form: E = 3.64 × 10^-19 J Final answer: 3.64 × 10^-19 J per photon
Common mistakes to avoid
- Using wavelength directly without converting to frequency first
- Forgetting that h is in joule-seconds, so the frequency must be in hertz (s^-1)
- Mixing up energy per photon with the total energy of many photons
Did You Know?
Blue light's photons carry more energy than red, which is why ultraviolet, not infrared, causes sunburn.
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