Summary

The Standard Model of Particle Physics: A Triumph of Science

• Particles can have wave-like behaviour and waves can have particle-like behaviour
• Schrodinger’s wave equation forms the basis for describing and predicting the behaviour of electrons
• Max Born postulated that $|\psi|(x)^2$ is a probability density function
• A result of applying Schrodinger’s wave equation to a bound particle is that the energy of the bound particle is quantized
  • Similarly, applying the wave equation to an electron incident on a potential barrier is that there is a finite probability of tunneling
• The concept of quantum numbers was developed from the results of applying Schrodinger’s wave equation to the one-electron atom
• The basic structure of the periodic table is predicted by applying Schrodinger’s wave equation to the one-electron atom and using the Pauli exclusion principle

Principles of Quantum Mechanics

Energy Quanta

Photoelectric effect demonstrates inconsistency between experimental results and the classical theory of light

Photoelectric effect and maximum kinetic energy if the photoelectron as a function of incident frequency

• According to classical physics, if the intensity of the light is large enough, an electron will be emitted form the surface independent of the incident frequency

• Maximum kinetic energy of the photoelectron varies linearly with frequency with a limiting frequency of $v = v_0$

  • If the incident intensity varies at a constant frequency, the rate of photoelectron emission changes, but the maximum kinetic energy remains the same

• Planck postulated that thermal radiation is emitted from a heated surface in discrete packets of energy called quanta

• The particle-like packet of energy is called a photon, whose energy is given by the following

  $$ E = hv \newline h = 6.625 \times 10 ^{-34} \space \text{[J-s]} $$

• The minimum energy required to remove an electron is called the work function of the material and any excess photo energy goes into the kinetic energy of the photoelectron

  • The photoelectron effect shows the discrete nature of the photo and demonstrates the particle-like behaviour of the photon

  $$ T = \frac{1}{2}mv^2 = hv - \Phi = hv -hv_0 \space (v \geq v_0) $$

  • Where $hv$ is the incident photon energy and $\Phi = hv_0$ is the minimum energy/work required to remove an electron from the surface

Wave-Particle Duality

Particle-like behaviour of EM waves was also in explanation of the Compton effect

• X-ray beam was incident on a solid, portion of the x-ray beam was deflected and the frequency of the deflected wave had shifted compared with the incident wave