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The **photon energy equation**, represented as E = h f, relates the energy (E) of a photon to Planck’s constant (h) and the frequency (f) of the photon. This equation allows for the calculation of the energy carried by a photon based on its frequency.

## Practice problems

### Problem #1

Calculate the energy of a photon with a frequency of 4.54 × 10^{6} Hz. Take the value of Planck’s constant as 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

Applying the formula:

- 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. Determine the energy of the photon. Take the values of Planck’s constant as h = 6.626 × 10^{-34} J s and the speed of light as 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

Applying the formula:

- 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

Calculate the energy of a photon with a frequency of 2.35 × 10^{9} Hz. Take the value of Planck’s constant as h = 6.626 × 10^{-34} J s.

**Solution**

Given data:

- Energy of a photon, E = ?
- Frequency of a photon, f = 2.35 × 10
^{9}Hz - Planck’s constant, h = 6.626 × 10
^{-34}J s

Applying the formula:

- 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

Determine the energy of a photon with a wavelength of 750 nm. Take the values of Planck’s constant as h = 6.626 × 10^{-34} J s and the speed of light as 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

Applying the formula:

- 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**.

## 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
**Photon energy equation**- Conservation of energy formula

## External links

- https://www.omnicalculator.com/physics/photon-energy
- https://study.com/learn/lesson/photon-energy-momentum-equation-calculation.html
- https://sciencing.com/calculate-energy-photons-5948572.html

Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.