Energy And Momentum Of A Photon (Copy)

Nature of Electromagnetic Radiation

• Electromagnetic (EM) radiation exhibits wave–particle duality:
  • Behaves like a wave: interference, diffraction.
  • Behaves like a particle: photoelectric effect, Compton scattering.
• A photon is a quantum (discrete packet) of electromagnetic energy.
• This is the foundation of quantum physics — energy transfer is not continuous but quantised.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

1. Definition of a Photon

• A photon is the smallest unit (quantum) of electromagnetic energy.
• It carries energy and momentum, but has no rest mass.
• All EM radiation (e.g. light, X-rays, gamma rays) is made of photons.

2. Energy of a Photon

• The energy of a photon is directly proportional to the frequency of the radiation.

Formula:

E = hf

Where:

• E = energy of the photon (Joules)
• h = Planck’s constant = 6.63 × 10⁻³⁴ J·s
• f = frequency of the radiation (Hz)

Alternate form using wave speed:

Since f = c / λ, we can also write:
E = hc / λ

Where:

• c = speed of light = 3.00 × 10⁸ m/s
• λ = wavelength of radiation (m)

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

3. The Electronvolt (eV)

• A practical unit of energy used in atomic and particle physics.

Definition:

• 1 electronvolt (1 eV) is the energy gained by an electron when it is accelerated through a potential difference of 1 volt.

Relationship:

1 eV = 1.60 × 10⁻¹⁹ J

Use:

• Convert photon energy from Joules to eV using:
  Energy (eV) = Energy (J) ÷ 1.60 × 10⁻¹⁹

4. Momentum of a Photon

• Although a photon has no mass, it still carries momentum due to its energy.

Formula:

p = E / c

Also using E = hf, we get:
p = hf / c

And since f = c / λ, we derive:
p = h / λ

Where:

• p = momentum (kg·m/s)
• E = energy (J)
• c = speed of light (m/s)
• h = Planck’s constant
• λ = wavelength of the photon (m)

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Summary Table

Real-World Example

Example: Find energy and momentum of a photon of wavelength 500 nm.

Step 1: Convert λ to meters:
λ = 500 × 10⁻⁹ m

Step 2: Use E = hc / λ:
E = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) / (500 × 10⁻⁹) = 3.978 × 10⁻¹⁹ J

Convert to eV:
E = 3.978 × 10⁻¹⁹ ÷ 1.60 × 10⁻¹⁹ = 2.49 eV

Step 3: Use p = h / λ:
p = 6.63 × 10⁻³⁴ / (500 × 10⁻⁹) = 1.33 × 10⁻²⁷ kg·m/s

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course