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How to Calculate Light Energy?

Published in Photon Energy 2 mins read

Light energy, also known as photon energy, can be calculated using specific formulas that relate energy to the light's frequency or wavelength. The appropriate formula depends on which property of light is known.

Understanding the Formulas

There are two primary formulas to determine the energy of light:

  • Using Frequency:

    • If you know the frequency (f) of the photon, you use Planck's equation: E = hf
      • E represents the energy of the photon.
      • h is Planck's constant (approximately 6.626 x 10^-34 joule-seconds).
      • f is the frequency of the photon in Hertz.
    • As noted in reference 1, Max Planck proposed this equation and it is known as Planck's equation.
  • Using Wavelength:

    • If you know the wavelength (λ) of the photon, you use the formula: E = hc/λ
      • E represents the energy of the photon.
      • h is Planck's constant (approximately 6.626 x 10^-34 joule-seconds).
      • c is the speed of light (approximately 3 x 10^8 meters per second).
      • λ is the wavelength of the photon in meters.
      • As mentioned in reference 2, you can calculate the photon's energy using this formula.

Calculation Examples

Let's explore how to apply these formulas with examples:

Example 1: Calculating Energy with Frequency

Suppose we have a photon with a frequency of 5 x 10^14 Hz. To find its energy:

  1. Use the formula: E = hf
  2. Plug in the values: E = (6.626 x 10^-34 Js) * (5 x 10^14 Hz)
  3. Calculate: E = 3.313 x 10^-19 joules.

Example 2: Calculating Energy with Wavelength

Consider a photon with a wavelength of 600 nm (600 x 10^-9 meters). To find its energy:

  1. Use the formula: E = hc/λ
  2. Plug in the values: E = (6.626 x 10^-34 Js) * (3 x 10^8 m/s) / (600 x 10^-9 m)
  3. Calculate: E = 3.313 x 10^-19 joules.

Practical Insights

  • Higher Frequency/Shorter Wavelength = Higher Energy: Light with higher frequency (e.g., ultraviolet light) or shorter wavelength (e.g., x-rays) carries more energy than light with lower frequency (e.g., radio waves) or longer wavelength (e.g., infrared).
  • Units are Crucial: Ensure all units are consistent. Frequency should be in Hertz, wavelength in meters, and energy will be in Joules.
  • Planck's Constant: Understanding Planck's constant is foundational in quantum mechanics, and is key to understanding light's behavior at a quantum level.

Summary

In summary, the formula E=hf is used when frequency is known, and the formula E=hc/λ is used when the wavelength is known. Both methods give the energy of a photon.