Photon Energy

In our previous session, we learned about photons. Photons are the massless particles of light. They are the packets of energy that constitute the electromagnetic spectrum. Photons are generated when electromagnetic waves emitted by a source encounter matter, they may absorb and transfer their energy. Hence, photons can be created as well as destroyed while conserving energy and momentum.

Photons move at the speed of light in a vacuum. A beam of light carries many photons. These are discrete particles of light. Every particle of the photon carries energy. When the frequency is more, the energy of the photon is more. In this session, let us learn about photon energy and its formula.

What is Photon Energy?

We know photons carry their own energy. The amount of energy is proportional to the electromagnetic frequency of the photon, and hence it is inversely proportional to the wavelength.

If the frequency of the photon is high, its energy will also be high. Hence, we can say if the wavelength of the photon is longer, the energy is lower.

We can say that an intense red light has the ability to carry more power to a given area than less intense blue light. We know that photon energy is expressed in the electronvolt (eV) unit and the joule.

The energy of the photon is given by the formula:

E = hf

Where,

• E = photon energy
• h = Planck’s constant
• f = The electromagnetic frequency measured in Hertz or Hz

The above formula is applicable to a single photon. When more photons are emitted, consider n number of photons, then the formula is given by:

E = n × h × f

Energy is calculated in Joules and electronvolt (eV), depending on the system of the unit used.

1 Joule = 6.24 × 10¹⁸ eV

For radiations like gamma rays, the large units help in representing the photon energy with higher energy and frequency.

Photon Energy Formula

We know that the speed of light (c) is constant in the vacuum. Hence, more photons of high frequency like gamma rays and X-rays travel at absolutely the same speed as low-frequency photons, like infrared radiations. When the frequency of a photon increases, the wavelength decreases. When the frequency decreases, the wavelength increases. The equation that relates these parameters for photons is given as below:

Since wavelength and frequency are interdependent parameters, the equation for the energy contained in a photon is given by:

E = hf or E = hc/λ

Where,

E = energy of the photon

h = Planck’s constant (6.62607015) × 10-34 J.s or kg m² s⁻¹)

f = photon frequency

λ = photon wavelength

c = speed of light (3 x 10⁸ meters/second)

The photon energy at 1 Hz is equal to 6.626 × 10⁻³⁴ J and the Planck’s constant in terms of eV is 4.14 × 10⁻¹⁵ eV· s.

Read more: Photon energy formula

Energy in Electronvolts

We know that energy is often measured in electron volts. To find the photon energy in electronvolts using the wavelength in micrometres, the equation is approximately

The above equation only holds if the wavelength is measured in picometers. The photon energy at 1 μm wavelength, the wavelength of near-infrared radiation, is approximately 1.2398 eV.

Note: Photoelectric effect was explained by the great scientist Einstein in the year 1905. This effect was explained using the discrete nature of light. The photoelectric effect was demonstrated using the shining surface of the metal surface. When the frequency of the light is higher than the cutoff frequency fc, electrons are emitted from the metal surface, and no electrons are emitted when the frequency is less than cutoff frequency fc.

Kinetic Energy of Photon Formula

From the Photoelectric effect, we know that electrons are tightly bound to the metal surface. In the photoemission process, electrons emitted have some energy. The maximum kinetic energy of ejected electrons is given by the formula:

Here,

E = photon energy

BE = binding energy or the Work function of the electron, which is particular to the given material.

The kinetic energy of photoelectron and frequency of incident light is given by the from

The energy of a photon depends on the following parameters:

• Photon’s energy is directly related to the photon’s electromagnetic frequency.
• Photon’s energy depends on wavelength in such a way that the energy of the photon is inversely proportional to the wavelength.
• The higher the photon energy frequency, the higher its energy. In contrast, the longer the photon’s wavelength, the lower its energy.

The invention of photon and photon energy has led to the quantum revolution in Physics. The concept of the photoelectric effect put forth by the great scientist Albert Einstein was awarded the Nobel Prize in the year 1922.

Hope you have understood photon energy and its formula. Stay tuned to BYJU’S to know more about various interesting Science and Math concepts.

Watch the video below to understand Hertz and Lenard’s Observation of Photoelectric Effect