ENERGY OF A PHOTON:

The Properties of Light," light was discussed as waves. Light must be treated as waves in order to examine its propagation through space, the operation of certain optical components, and to explain phenomena such as polarization, coherence, and interference. The wave nature of light is not normally used to explain the emission and absorption of light by atoms. In these processes, light can be described as behaving more like a particle than a wave, i.e., light seems to consist of tiny entities, each with its own characteristic energy content. The "duality principle" of light states that "light cannot be described completely as either a particle or a wave, but has characteristics of both," i.e., there is a complementarily of the two concepts.
A photon is the smallest division of a light beam that retains the properties of the beam. The characteristics of a photon include its frequency, its wavelength, and its energy. A photon should not be visualized as a particle that has physical dimension or a specific location in space. More accurately, a photon can be considered a "wave packet" that has a specific energy content.
PLANCK S CONSTANT:
Energy = h*Frequency

The energy of a photon is directly proportional to the frequency of the photon and is given by Equation 1.
Equation 1
E = h?
where: E = Energy of photon in joules (J).
? = Frequency of the photon in hertz.
h = Planck s constant = 6.625 × 10–34 joule-seconds.

EXAMPLE A: CALCULATION OF THE ENERGY OF A PHOTON OF GIVEN FREQUENCY
Given: The frequency of a photon of HeNe laser light is 4.74 × 1014 Hz.
Find: The energy of the photon.
Solution: E = h?
E = (6.625 × 10–34 J.sec) (4.74 × 1014/sec)
E = 3.14 × 10–19 J
The frequency of a photon is determined by the relation described by Equation 2.
Equation 2

where: c = The speed of light in vacuum, namely 3 × 108 m/sec.
? = Wavelength in meters.
Substitution of Equation 2 into Equation 1 yields Equation 3.
Equation 3






EXAMPLE B: CALCULATION OF THE ENERGY OF A PHOTON OF A GIVEN WAVELENGTH
Given: The wavelength of a He-Ne laser light is 633 nm.
Find: The energy of the photon of this light.
Solution:
Equations 1, 2, and 3 can be used to determine the frequency, wavelength, or energy of a photon if any one of these quantities is known. Example C is a further illustration of the use of these equations.
EXAMPLE C: CALCULATION OF WAVELENGTH AND FREQUENCY OF A PHOTON OF GIVEN ENERGY
Given: A photon has an energy of 1.875 × 10–19 J.
Find: The frequency and the wavelength of the photon.
Solution: From Equation 1

From Equation 2—

ENERGY UNITS:
The unit of energy used in Planck s constant and in the preceding examples is the joule (J). The joule is the basic energy unit in the International System of Units (sometimes referred to as the MKS system—meters, kilograms, seconds) and is the amount of energy necessary to raise one kilogram mass (2.2 lb) to a height of 10.2 cm against the pull of gravity.
Another common energy unit used when talking about electron motion in atoms, energy levels in atoms, and photon energy, is the electron volt (eV). It is defined as the amount of energy acquired by an electron, when it is accelerated by a potential difference of one volt, hence the name "electron volt." One electron volt of energy is equal to 1.602? 10-19 joules of energy, that is, 1eV = 1.602? 10-19J.
The counterpart of the energy unit joule in the centimeter-gram-second system of units (the CGS system as opposed to the MKS system,) is the erg. The erg is a very small unit of energy. It takes ten million ergs to equal one joule of energy (1 erg=10-7J.) In the study of laser optics, you will rarely have to involve ergs in your calculation, but you may run across them in tables or scientific articles, so it s good to know they exist.
The energy units most commonly used to specify the energy of photons, electrons and atoms, are the joule (J) and electron volt (eV). Another unit, called a Wavenumber, is used often by spectroscopists to denote atomic and molecular energy levels. But, as the next section shows, it is not a true energy unit, even though it is useful as an indicator of energy values.
The Wavenumber of a photon is the number of wavelengths of that photon contained in a length of one centimeter. The Wavenumber is given by Equation 4. Here we use the symbol k to represent the Wavenumber in cm-1. It is perhaps