Photon Energy Formula

The photon is a fundamental particle that acts as the fundamental of the electromagnet, which includes electromagnetic waves like light and radio frequencies, as well as the electromagnetic force's force carrier. Because photons have no mass, they always travel at speeds of light in a vacuum. 

Photon Energy

The energy contained in one photon is referred to as photon energy. The photon's electric and magnetic wavelength is dependent on the amount of energy it contains, and consequently, the wavelength is inversely proportionate. In other words, the longer the wavelength of a photon, the lesser its energy and vice-versa. Any unit of energy can be used to express photon energy. The electronvolt (eV) and the joule are two typical units for measuring photon energy. 

To put it simply, light generates a stream of power known as photons, each of which contains its own energy called photon energy. 

Formula

E = hc/λ 

where,

• h is Planck's constant (6.626 × 10⁻³⁴ Js)
• c denotes the speed of light (3 × 10⁸ m/s)
• λ denotes the wavelength 

Sample Problems

Problem 1. Find the photon energy for a wavelength of 650 nm.

Solution:

Given: λ = 650 nm, c = 3 × 10⁸ m/s and h = 6.626 × 10⁻³⁴  Js

Since, E = hc/λ

= 6.626×10⁻³⁴ × 3×10⁸ / 650×10⁻⁹

= 19.878×10²⁸ / 650×10⁻⁹

E = 0.030 × 10⁻¹⁷ J

Problem 2. Find the photon energy for a wavelength of 750 nm.

Solution:

Given: λ = 750 nm, c = 3 × 10⁸ m/s and h = 6.626 × 10⁻³⁴  Js

Since, E = hc/λ

= 6.626×10⁻³⁴ × 3 ×10⁸ / 750 × 10⁻⁹

= 19.878×10^–42 / 750×10⁻⁹

E = 2.65 x 10¹⁹ J

Problem 3. Find the wavelength if the photon energy is 350 x 10^-10 J.

Solution:

Given: E = 350 x 10^-10 J, c = 3 × 10⁸ m/s and h = 6.626 × 10⁻³⁴  Js

Since, E = hc/λ ⇒ λ = hc/E

= 6.626×10⁻³⁴ × 3 × 10⁸ / 350×10⁻¹⁰

= 19.87×10^-28 / 350×10⁻¹⁰

λ = 0.056 × 10^-16 m

Problem 4. Find the wavelength if the photon energy is 200 × 10^-10 J.

Solution:

Given: E = 200 x 10^-10 J, c = 3 × 10⁸ m/s and h = 6.626 × 10⁻³⁴  Js

Since, E = hc/λ ⇒ λ = hc/E

= 6.626×10⁻³⁴ × 3 × 108 / 200×10⁻¹⁰

= 19.87×10^-28 / 200×10⁻¹⁰

λ = 1.56 × 10^-16 m

Problem 5. Find the photon energy for a wavelength of 350 nm.

Solution:

Given: λ = 350 nm, c = 3 × 108 m/s and h = 6.626 × 10−34  Js

Since, E = hc/λ

= 6.626×10−34 × 3 ×108 / 350 × 10−9

= 19.878×10–42 / 350×10−9

E = 0.32 × 10¹⁹ J