How to calculate the energy of a photon given wavelength

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Light is an electromagnetic wave that carries energy across space. The Energy per unit area and unit time is defined as intensity which is directly proportional to the square of the amplitude of the electric field of the light wave. This energy is not continuous but arrives in discrete units called photons. Photons are the particles of light.  

Photon Properties

Photons have a number of Properties which are:

• Photons are electrically neutral.
• Photons velocity equals the speed of light.
• Photons are massless, but they have energy E = hf = hc/λ.  Here h = 6.626*10-34 Js is called Planck's constant.  The photon energy is inversely proportional to the wavelength of the electromagnetic wave.  The shorter the wavelength, the more energetic is the photon, the longer the wavelength, the less energetic is the photon.
• Photons can be created and destroyed while conserving energy and momentum.  Photons are created when EM waves are emitted by a source and when they encounter matter, they may be absorbed and transfer their energy.
• Photoelectric effect was explained by, Einstein in 1905 using discrete nature of light.  It was demonstrated by shining light on a metal surface.  Electrons are released if the frequency of the light is higher than the cutoff frequency fc, while no photoelectric electrons are emitted if the frequency of the light falls below this cutoff frequency fc.
• Photon wavelength: 0.377 um or 377 nm. Photon energy: 3.2883eV.

Equations for Photon

A photon is described by either λ  which is the wavelength, or by E which is the Energy. The relationship between the energy of a photon (E) and the wavelength of the light (λ) is an inverse relationship and is described by the following by the equation: E=hcλE=hcλ where h is Planck's constant and c is the speed of light. h = 6.626 × 10 -34 joule·sc = 2.998 × 108 m/s By multiplying to get a single expression, hc = 1.99 × 10-25 joules-m The above inverse relationship means that light consisting of high energy photons has a short wavelength. Light consisting of low energy photons has a long wavelength. eV ( Electron –volt) is the unit of energy commonly used when dealing the particles rather than joule (J). An electron volt is the energy required to move an electron through 1 volt, thus the energy of 1 eV for a photon is 1.602 × 10-19 J. So the above equation can be written by expressing constant for hc in terms of eV: hc = (1.99 × 10-25 joules-m) × (1ev/1.602 × 10-19 joules) = 1.24 × 10-6  eV-mFurther, the units should µm (the units for λ):hc = (1.24 × 10-6 eV-m) × (106 µm/ m) = 1.24 eV-µm By expressing the equation for photon energy in terms of eV and µm the energy and wavelength of a photon can be related, as shown in the following equation: E(eV)=1.24λ(μm)EeV=1.24λμm The exact value of 1 × 106(hc/q) is 1.2398 but the approximation 1.24 is sufficient for most purposes.

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.

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:

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

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

Planck's photo energy equation is:

E=hcλ=hf\small E = \frac{hc}{\lambda} = hfE=λhc​=hf

where:

• $E$ – Energy of a photon;
• $h$ – Planck constant;
• $c$ – Speed of light;
• $\lambda$ – 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.

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.