Photon energy equation

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Photon energy equation
Photon energy equation | Image: Learnool

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 × 106 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 × 106 Hz
  • Planck’s constant, h = 6.626 × 10-34 J s

Applying the formula:

  • E = h f
  • E = 6.626 × 10-34 × 4.54 × 106
  • 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 × 108 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 × 108 m/s

Applying the formula:

  • E = h c/λ
  • E = (6.626 × 10-34 × 3 × 108) ÷ (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 × 109 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 × 109 Hz
  • Planck’s constant, h = 6.626 × 10-34 J s

Applying the formula:

  • E = h f
  • E = 6.626 × 10-34 × 2.35 × 109
  • 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 × 108 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 × 108 m/s

Applying the formula:

  • E = h c/λ
  • E = (6.626 × 10-34 × 3 × 108) ÷ (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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External links

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.

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