Tiny particles are affected in different ways than we are by waves. There are several different effects that must be discussed.

The Photoelectric Effect

Many people believe that Albert Einstein won the Nobel Prize for his discovery of special relativity, as that is what he is most well-known for. However, his actual claim to fame in that respect had to with the photoelectric effect. He found that when light of a certain wavelength is incident on certain metals, electrons are ejected from the surface of the metal.

The number of photoelectrons emitted, the photocurrent, increases with intensity, though the kinetic energy does not. The kinetic energy only increases with an increase in energy of the light i.e. a decrease in the wavelength. Above a certain wavelength, no electrons are ejected.

$$ \frac{hc}{λ_0} = W_0 + KE_{max} $$

where \(W_0\) is the work function for the metal in question. You can think of it as an intrinsic quality of the metal. \(λ_0\) is the cutoff wavelength after which no more electrons will be ejected.

Pair Production/Annihilation

When a high energy photon collides with a nucleus, it may "split" into an electron and a positron. When this split happens, the charge, momentum, and the mass-energy of all parties must be conserved:

$$ E_{photon} = KE_{positron} + KE_{electron} + 2E_0 $$

where \(E_0\) is the rest mass-energy for each particle given by \(E = mc^2\), doubled since the electron and positron are identical.

The opposite operation can occur when an electron and a positron combining will annihilate the pair and create two identical photons with opposite momentum. The reason that there must be two photons and not just one is that the momentum must equal 0, so there has to be opposite momentum.

de Broglie Wavelength

All particles exhibit wave-like characteristics, which can be demonstrated by the double-slit experiment. The wavelength of a particle in this instance can be determined from the following equation:

$$ λ = \frac{h}{p} = \frac{h}{mv} = \frac{h}{\sqrt{2mKE}} $$

The wavelength of a photon is a little different, since photons are completely massless. The momentum and energy of a photon are related by a simpler equation \(E = pc\), which applies to all massless particles, not just photons.

Uncertainty

One key problem for physicists studying particles is the Heisenberg Uncertainty Principle. In layman's terms, the observation of a particle fundamentally changes its quality, so it can never be truly measured. In mathematical terms, the accuracy of a measurement of a position's momentum and position at the same time is limited:

$$ (Δp_y)(Δy) ≥ \frac{h}{4π} $$

and the same function exists for simultaneous measurements of energy and time.