Chapter 3.8: Spin
Electromagnetism and Spin in Classical Physics
Charged particles create magnetic fields when in motion.
Example: An electron moving in a straight line generates a magnetic field around it.
Current in a wire also generates a surrounding magnetic field.
Movement of charged particles in circular or looping paths results in magnetic fields that wrap around the routes.
Particle Motion and Magnetic Fields
Circular wire wrapped with a magnetic field interacts with the field around it.
Rotating Particles and Spin
A rotating charged particle also creates a wrapping magnetic field.
Behavior characterized by Maxwell's equations, specifically Ampère's Law.
Charged particles that loop or rotate act like tiny bar magnets.
Notably, particle spin is an intrinsic angular momentum, unrelated to a physical spinning motion.
Analogy: A gyroscope in a box demonstrates angular momentum without visible motion of the box itself.
Intrinsic vs. Extrinsic Properties
Intrinsic Properties: Inherent to the particle itself; examples include mass, charge, and spin.
Extrinsic Properties: Dependent on external factors; examples include velocity and kinetic energy.
The Nature of Electron Spin
Electrons cannot physically spin due to their minuscule size.
For a particle to physically spin and generate a magnetic field, its surface speed would exceed the speed of light.
Analogy: A skater with arms folded spins faster when smaller in size.
Stern-Gerlach Experiment Overview
Concept: A beam of uncharged particles in a magnetic field should not interact based on classical electromagnetism.
The Lorentz force: Force exerted by a magnetic field on a moving charge.
When silver atoms were used in the experiment, unexpected interference occurred, behaving like tiny magnets.
Inhomogeneous Magnetic Field: A field with varying strength and direction.
Observations from the Stern-Gerlach Experiment
Classical expectations were that particles would spread across a vertical path based on magnetic interaction.
Instead, particles were deflected into two distinct paths (upward or downward), indicating two states of intrinsic angular momentum (spin).
Silver atoms used have 47 electrons, with one unpaired electron contributing to the atom's spin and magnetic moment.
Spin Quantum Number
The experiment introduced the concept of spin quantization.
Spin is quantized: discrete values represent intrinsic angular momentum.
Particles categorized by spin quantum number (s) affecting their maximum angular momentum:
Electrons: Spin-1/2: two states (spin-up +1/2, spin-down -1/2).
Photons: Spin-1: three states (+1, 0, -1).
General formula: Number of states = 2s + 1.
Classification of Particles
Half-integer spin particles (e.g., electrons) are fermions.
Integer spin particles (e.g., photons) are bosons.
Spin quantum number is part of four quantum numbers defining an electron's unique quantum state in an atom.
Quantum Spin and Medical Imaging (MRI)
Spin influences MRI technology through nuclear magnetic resonance (NMR).
Key component: Hydrogen nuclei (protons), considering body water composition.
Step 1: Protons align with the magnetic field during MRI scanning.
Step 2: Radiofrequency (RF) pulses disrupt alignment, leading to energy emission as they realign.
Step 3: Contrast during imaging is based on relaxation rates of proton spins, resulting in T1 and T2 weighted images affecting appearances of fatty and watery tissues.