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# Photon Energy Formula

The concept of the photon is introduced by discussion of the process of electromagnetic field quantization within a closed cavity or in an open optical system. A photon is characterized by either a wavelength $\lambda$ or equivalently an energy E. Energy of a photon is inversely proportional to the wavelength of a photon. The formula for photon energy is given as,

Where E is the photon energy, h is the Planck's constant (6.626$\times10^{-34}$ Js), c is the speed of the light and $\lambda$ is the wavelength of the light.

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## Photon Energy Problems

Let us discuss the problems related to the photon energy.

### Solved Examples

Question 1: Calculate the photon energy if the wavelength is 640nm?

Solution:

Given parameters are,
$\lambda$ = 640nm
We know the values of c and h; c = 3$\times10^{8}$m/s and h = 6.626$\times10^{-34}$Js
Photon energy formula is,

E = $\frac{hc}{\lambda}$

E = $\frac{6.626\times10^{-34}\times3\times10^{8}}{640\times10^{-9}}$ = 0.031$\times10^{-17}$J

Question 2: If the energy of a photon is 350$\times10^{-10}$J, calculate the wavelength of that photon?

Solution:

Given parameters are,
E = 350$\times10^{-10}$J
We know the values of c and h; c = 3$\times10^{8}$m/s and h = 6.626$\times10^{-34}$Js
Photon energy formula is,

E = $\frac{hc}{\lambda}$

So, $\lambda$ = $\frac{hc}{E}$

$\lambda$ = $\frac{6.626\times10^{-34}\times3\times10^{8}}{350\times10^{-10}}$ = 0.056$\times10^{-16}$m

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