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# Energy of Photon

#### Definition

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·s c = 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-m Further, 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.
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