## What is energy of photon in light ?

Photon energy 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 us understand how to calculate photon energy based on light wavelength or frequency in following two light energy calculators.

### Photon energy Calculator #1 using light wavelength

Following calculator calculates photon energy based on light wavelength.

Example Photon Energy calculator #1:

INPUTS : Light wavelength = 0.5 µm

OUTPUTS: Photon Energy = 3.97566 e-19 Joule

### Energy of light formula or e = hv equation

Following formula or equation is used to calculate energy of photon.
This calculator calculates photon energy based on walelength of the light source.
The e = hv is known as Planck's equation. The photon frequency (v) is the ratio of speed of light and light wavelength.
Speed of light equals 3 x 10^{8} 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.

### How to calculate photon energy using light frequency

Following calculator #2 calculates energy of photon based on light frequency.

Example Photon Energy calculator #2:

INPUTS : Light wavelength = 300 GHz

OUTPUTS: Photon Energy = 1.98 x 10^{-22} Joule

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

➨ N = P in Watts/E in Joules

Example: If P is 1 Watts and Energy of each photon is 4 x 10^{-19} , then
number of emitted photons in one second is equal to 2.5 x 10^{8}.

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 formula, E = hν (or E = hc/λ), relates the energy (E) of a photon to its frequency (ν) or wavelength (λ).