Last updated: Apr 14, 2024

Photon Energy Calculator

Q: What is the energy of a photon with wavelength 450 nm?

The energy of this photon is 2.75 eV . To find this result: Find the frequency : divide the speed of light by the wavelength: f = 3E9 m/s/4.50E-7 m = 666.2E12 Hz = 666.2 THz Multiply the frequency by Planck's constant: E = h × f = 666.2E12 Hz × 6.626E-34 m²-kg/s = 4.41E-19 J Divide this result by the charge of the electron, e , to find the energy in electronvolts : E [ev] = E [J]/e = 2.75 eV That's it! Read more

Table of contents

Planck's equation How to calculate the energy of a photon Energy of a photon calculator FAQs

With this photon energy calculator, you can explore the relationship between the wavelength and frequency of the photon and its energy. Read the text below to find out how to calculate the energy of a photon and what is Planck's equation.

Planck's equation

The light seems to us to have a wavy character. It diffracts, interferes, and refracts. However, at a microscopic level, it is carried by a minuscule quantum of energy called the photon. The energy of a photon depends solely on its wavelength or frequency. Because light travels, well, at the speed of light, we can use either frequency or wavelength to describe it. You can check the wavelength calculator to explore the relationship between the wavelength and frequency.

Coming back to photons, what is their energy? The energy of a single photon is a tiny number given by Planck's equation. Planck's equation relates the frequency of a photon to its energy through a Planck constant $h$ equal to:

\small h = 6.6261 \times 10^{-34}\ \text{J}\!\cdot\!\text{s}

The Planck constant is in the units (energy)·(time), and you can think of it as a conversion factor from energies to frequencies.

💡 You might also be interested in the photoelectric effect calculator.

How to calculate the energy of a photon

Planck's photo energy equation is:

\small E = \frac{hc}{\lambda} = hf

where:

$E$ – Energy of a photon;
$h$ – Planck constant;
$c$ – Speed of light;
$λ$ – Wavelength of a photon; and
$f$ – Frequency of a photon.

This equation gives us the energy of a single, indivisible quanta of light, and we can think of light as a collection of particles. The opposite is also true. We can think about ordinary particles, like electrons, as waves. Check De Broglie wavelength calculator to learn more about this concept.

Energy of a photon calculator

The energy of a single photon is a small number because the Planck constant is ridiculously tiny. The energy of a single photon of green light of a wavelength of 520 nm has an energy of 2.38 eV. You can use the photon energy calculator to explore further the relationship between the photon energy and its frequency or wavelength.

FAQs

How do I calculate the energy of a photon?

To calculate the energy of a photon, follow these easy steps:

If you know the wavelength, calculate the frequency with the following formula:
f =c/ λ
where c is the speed of light, f the frequency and λ the wavelength.
If you know the frequency, or if you just calculated it, you can find the energy of the photon with Planck's formula:
E = h × f

where h is the Planck's constant: h = 6.62607015E-34 m² · kg/s
3. Remember to be consistent with the units!

Which photons are the most energetic?

Photons with shorter wavelengths are more energetic: a shorter wavelength corresponds to a higher frequency, and, thanks to Planck's formula E = h × f, we know that the frequency is directly proportional to the energy.

The region of the spectrum that contains the most energetic photons is the one associated with ionizing radiations. From extreme ultraviolet light to X-rays, we arrive at gamma rays, the most energetic radiation known to scientists.

What is the energy of a photon with wavelength 450 nm?

The energy of this photon is 2.75 eV. To find this result:

Find the frequency: divide the speed of light by the wavelength:

f = 3E9 m/s/4.50E-7 m = 666.2E12 Hz = 666.2 THz
Multiply the frequency by Planck's constant:

E = h × f = 666.2E12 Hz × 6.626E-34 m²-kg/s = 4.41E-19 J
Divide this result by the charge of the electron, e, to find the energy in electronvolts:

E [ev] = E [J]/e = 2.75 eV

That's it!

What are the energies of photons in the electromagnetic spectrum?

The energies of photons in the electromagnetic spectrum vary widely:

Extremely low frequencies radio waves have energies in the order of the femtoelectronvolt. Their wavelengths can reach millions of meters!
"Normal" radio waves (the ones of FM stations) have energies of hundreds of nano electronvolts.
The visible light has energies from ~1.5 eV to 3.3 eV.
X-rays are at least one thousand times more energetic than visible light, lying in the keV range.
Gamma rays, the most energetic EM radiation, has energies above the megaelectronvolt: damage is sure if they hit any material!