Wave-Particle Duality of Light

Electromagnetic radiation behaves as both a particle and a wave known as Wave-Particle Duality. The waves associated the particles are called Matter Waves. In order for the electron to maintain moment, the perimeter of its orbit must be a multiple of its wavelength.

The energy of a photon (no rest mass) is given by the following formula:

\(E = hf\)

Where:

• \(E\) is the energy
• \(h\) is Planck's constant
• \(f\) is the frequency

NOTE: Planck's constant can be represented as either \(6.626 \cdot 10^{-34} [\text{m}^2 \cdot \text{kg/s}]\) or \(4.136 \cdot 10^{-15} [\text{eVs}]\).

The wavelength is given by the following formula:

\(\lambda = \cfrac{hc}{E}\)

Where:

• \(\lambda\) is the wavelength
• \(h\) is Planck's constant
• \(c\) is the speed of light (\(3.0 \times 10^8 [\text{m/s}]\))
• \(E\) is the energy

The momentum is given by the following formula:

\(p = \cfrac{E}{c}\)

Where:

• \(p\) is the momentum
• \(E\) is the energy
• \(c\) is the speed of light (\(3.0 \times 10^8 [\text{m/s}]\))

Compute the wavelength of a \(1 \; [\text{MeV}]\) photon.