**Photon energy** (E) is the product of **planck’s constant **(h) and the **frequency** (f). Using the equation of photon energy: **E = h f**, the value of energy of a photon can be calculated.

Let’s solve some problems based on this equation, so you’ll get a clear idea.

## Photon Energy Practice Problems

**Problem 1:** Calculate the energy of a photon which is having a frequency of 4.54 × 10^{6} Hz. (Take the value of planck’s constant, h = 6.626 × 10^{-34} J s)

Solution:

Given data:

Energy of a photon, E = ?

Frequency of a photon, f = 4.54 × 10^{6} Hz

Planck’s constant, h = 6.626 × 10^{-34} J s

Using the equation of photon energy,

E = h f

E = 6.626 × 10^{-34} × 4.54 × 10^{6}

E = 30.08 × 10^{-28} J

Therefore, the energy of a photon is **30.08 × 10 ^{-28} J**.

**Problem 2:** A photon has a wavelength of 450 nm. Calculate the energy of a photon. (Take the value of planck’s constant, h = 6.626 × 10^{-34} J s and speed of light, c = 3 × 10^{8} m/s)

Solution:

Given data:

Wavelength of a photon, λ = 450 nm = 450 × 10^{-9} m

Energy of a photon, E = ?

Planck’s constant, h = 6.626 × 10^{-34} J s

Speed of light, c = 3 × 10^{8} m/s

Using the equation of photon energy,

E = h c/λ

E = (6.626 × 10^{-34} × 3 × 10^{8}) ÷ (450 × 10^{-9})

E = 0.0441 × 10^{-17} J

Therefore, the energy of a photon is **0.0441 × 10 ^{-17} J**.

**Problem 3:** A photon has a frequency of 2.35 × 10^{9} Hz. Calculate the energy of a photon. (Take the value of planck’s constant, h = 6.626 × 10^{-34} J s)

Solution:

Given data:

Frequency of a photon, f = 2.35 × 10^{9} Hz

Energy of a photon, E = ?

Planck’s constant, h = 6.626 × 10^{-34} J s

Using the equation of photon energy,

E = h f

E = 6.626 × 10^{-34} × 2.35 × 10^{9}

E = 15.57 × 10^{-25} J

Therefore, the energy of a photon is **15.57 × 10 ^{-25} J**.

**Problem 4:** Calculate the energy of a photon which is having a wavelength of 750 nm. (Take the value of planck’s constant, h = 6.626 × 10^{-34} J s and speed of light, c = 3 × 10^{8} m/s)

Solution:

Given data:

Energy of a photon, E = ?

Wavelength of a photon, λ = 750 nm = 750 × 10^{-9} m

Planck’s constant, h = 6.626 × 10^{-34} J s

Speed of light, c = 3 × 10^{8} m/s

Using the equation of photon energy,

E = h c/λ

E = (6.626 × 10^{-34} × 3 × 10^{8}) ÷ (750 × 10^{-9})

E = 0.0265 × 10^{-17} J

Therefore, the energy of a photon is **0.0265 × 10 ^{-17} J**.

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**Related:**

- Thermal Energy Equation
- Potential Energy Formula
- Gravitational Potential Energy Formula
- Electric Potential Energy Formula
- Elastic Potential Energy Formula
- Kinetic Energy Formula
- Rotational Kinetic Energy Formula
- Electrical Energy Equation
- Mechanical Energy Formula
- Conservation of Energy Formula

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