Photon Energy Calculator: E=hv Formula Explained

Photon energy, a fundamental concept in quantum physics, explains the energy of a photon as it relates to frequency. Using the E=hv formula (where E is energy, h is Planck’s constant, and v is frequency), scientists and engineers can calculate the energy carried by light at various frequencies.

This page dives into the photon energy equation, explains how to apply it, and includes a handy calculator for quick calculations.

What is Photon Energy?

It refers to the energy carried by a single photon, which is a quantum of electromagnetic radiation such as light. Photons are particles of light and other electromagnetic waves. They have both wave-like and particle-like properties and are considered quantized packets of energy. The energy of a photon depends on its frequency (ν) or, equivalently, its wavelength (λ).

The relationship between photon energy (E), frequency, and wavelength is described by the following equations.

• Using Frequency (ν): E = hν
• Using Wavelength (λ): E = hc/λ

Where:

• E is the energy of the photon (in joules, J).
• h is Planck’s constant, approximately 6.626 x 10^-34 J·s.
• c is the speed of light in a vacuum, approximately 299,792,458 meters per second (m/s).
• ν (nu) is the frequency of the photon (in hertz, Hz).
• λ (lambda) is the wavelength of the photon (in meters, m).

Let’s understand how to calculate photon energy based on light wavelength or frequency in the following two light energy calculators.

Photon Energy Calculator using light wavelength

Example #1:

• INPUTS: Light wavelength = 0.5 µm
• OUTPUTS: Photon Energy = 3.97566 e-19 Joule

Energy of Light Formula or e=hv Equation

The following formula or equation is used to calculate the energy of a photon. This calculator calculates photon energy based on the wavelength of the light source.

The e=hv is known as Planck’s equation. The photon frequency (v) is the ratio of the speed of light and light wavelength. Speed of light equals 3 x 10⁸ meters/second.

These equations show that the energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. In simple terms, photons with higher frequencies (shorter wavelengths) have more energy, while photons with lower frequencies (longer wavelengths) have less energy. This is a fundamental concept in quantum physics, explaining how the energy of electromagnetic radiation is quantized into discrete packets when observed at the quantum level.

Photon Energy Calculator using light frequency

Example #2:

• INPUTS: Light frequency = 300 GHz
• OUTPUTS: Photon Energy = 1.98 x 10^-22 Joule

If the light source power is given as P (in Watts) and each photon energy is E in joules, the number of photons (N) emitted per second can be calculated using the following equation:

• N = P in Watts / E in Joules

Example: If P is 1 Watt and the Energy of each photon is 4 x 10^-19, then the number of emitted photons in one second is equal to 2.5 x 10¹⁸.

Conclusion

The equation is fundamental in quantum physics and helps explain that the energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength.

The photon energy equation, E = hν (or E = hc/λ), relates the energy (E) of a photon to its frequency (ν) or wavelength (λ). It is essential for work in fields like quantum mechanics, spectroscopy, and photonics. Using this, we can precisely determine the energy of photons across frequencies, enabling accurate analysis and research in various scientific applications.