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Modern Physics and Applications

Subject: Physics
Topic: 10
Cambridge Code: 0625

Special Relativity​

Relativity - Physics at very high speeds approaching light speed

Constancy of Light Speed​

Speed of light in vacuum (c): c=3×108 m/s (constant)c = 3 × 10^8 \text{ m/s (constant)}

  • Same in all reference frames
  • Maximum possible speed
  • Nothing can exceed it

Time Dilation​

Time passes slower at high speeds:

t=t01−v2/c2=γt0t = \frac{t_0}{\sqrt{1 - v^2/c^2}} = γt_0

Where:

  • t = time observed
  • t₀ = proper time (at rest)
  • γ = Lorentz factor

Effect negligible at ordinary speeds Significant as v → c

Length Contraction​

Objects shorten along direction of motion:

L=L01−v2/c2L = L_0\sqrt{1 - v^2/c^2}

Where:

  • L = observed length
  • L₀ = rest length

Mass and Energy​

Mass-Energy Equivalence​

E=mc2E = mc^2

Implications:

  • Mass can convert to energy
  • Energy can create mass
  • Huge energy from tiny mass

Examples:

  • Nuclear reactions: small Δm → huge E
  • Electron-positron annihilation: m → 2 photons
  • Pair production: photon → e⁺e⁻

Medical Physics​

X-ray Production​

X-rays from:

  1. Bremsstrahlung: Decelerating electrons (continuous spectrum)
  2. Characteristic X-rays: Electron transitions between levels

Properties:

  • High penetrating power
  • Ionizing (can damage tissue)
  • Stopped by high-Z materials (lead)

X-Ray Imaging​

X-ray tube:

  • Cathode (electron source)
  • Anode (target)
  • Vacuum tube

Image formation:

  • Dense materials (bone) absorb more → appear white
  • Soft tissue penetrates more → appear gray
  • Air penetrates completely → appears black

CT Scanning​

Computed Tomography:

  • Multiple X-ray images from different angles
  • Computer reconstructs 3D image
  • Better detail than single X-ray
  • Higher radiation dose

Ultrasound​

Ultrasound - Sound waves > 20 kHz (beyond human hearing)

Properties​

Wavelength: Short (can image small structures) Penetration: Limited (good for tissues) Safety: Non-ionizing (no radiation damage)

Imaging​

Echolocation principle:

  • Pulse sent into body
  • Reflects from boundaries
  • Delay indicates depth
  • Signal strength indicates density

Doppler ultrasound:

  • Frequency shift detects motion
  • Blood flow measurement
  • Fetal heartbeat

Nuclear Medicine​

Radioactive Tracers​

Tracers absorbed selectively:

  • Labeled with radioactive isotope
  • Gamma rays detected
  • Shows which tissues use the tracer

Examples:

  • Iodine-131 for thyroid
  • Technetium-99m for perfusion imaging

PET Scanning​

Positron Emission Tomography:

  • Positrons annihilate electrons
  • Produce gamma rays
  • Detected and image reconstructed
  • Shows metabolic activity

Laser Applications​

Laser Properties​

Coherent light:

  • All waves in phase
  • Single wavelength
  • Highly directional
  • High intensity

Medical Uses​

Laser surgery:

  • Concentrated energy cuts tissue
  • Cauterizes (seals blood vessels)
  • Minimal damage to surroundings
  • Examples: LASIK eye surgery, tumor removal

Photodynamic therapy:

  • Drug activated by laser light
  • Kills cancer cells
  • Minimizes normal tissue damage

Particle Physics​

Fundamental Particles​

Quarks: Building blocks of hadrons

  • Up, down, strange, charm, top, bottom
  • Carry fractional charge (±1/3 or ±2/3 e)

Leptons: Electrons, muons, neutrinos

  • Electron has charge -e
  • Neutrino has no charge

Hadrons​

Baryons: 3 quarks (odd number)

  • Protons, neutrons, lambda particles

Mesons: Quark-antiquark pairs

  • Pions, kaons
  • Unstable (decay)

Fundamental Forces​

Carried by exchange particles (bosons):

  1. Strong force: Quarks bound (gluons)
  2. Weak force: Beta decay (W, Z bosons)
  3. Electromagnetic: Photons
  4. Gravity: Gravitons (hypothetical)

Astrophysics​

Stellar Classification​

Hertzsprung-Russell diagram:

  • Horizontal: Temperature (spectrum)
  • Vertical: Luminosity (brightness)

Main sequence: Most stars Red giants: Old, large, cool White dwarfs: Dead stellar remnant

Star Life Cycle​

Birth: Cloud of gas collapses Main sequence: Hydrogen fusion Red giant: Helium fusion Death: Varies by mass

  • White dwarf (low mass)
  • Neutron star (high mass)
  • Black hole (very high mass)

Black Holes​

Event horizon: Point of no return Escape velocity > c: Nothing escapes Formed from: Massive star collapse

Renewable Energy​

Solar Energy​

Photovoltaic effect:

  • Photons create electron-hole pairs
  • Separated by electric field
  • Current generated

Solar thermal:

  • Direct heating of fluid
  • Used for water heating, electricity

Advantages: Clean, renewable, abundant

Wind Energy​

Kinetic energy of wind → mechanical → electrical

P=12Av3ρP = \frac{1}{2}Av^3ρ

Advantages: Clean, renewable Disadvantages: Intermittent, visual impact

Emerging Technologies​

Fusion Energy​

Promise:

  • Abundant fuel (hydrogen isotopes)
  • Clean (no greenhouse gas)
  • No long-lived radioactive waste
  • Safe (can't runaway like fission)

Challenge:

  • Extreme conditions needed (100+ million K)
  • Engineering difficulties
  • Not yet commercially viable

Quantum Computing​

Quantum bits (qubits):

  • Exist in superposition
  • Can be 0, 1, or both
  • Exponential computing power for certain problems

Promise:

  • Drug discovery
  • Optimization problems
  • Artificial intelligence

Sustainability​

Energy Conversion Efficiency​

Coal power: ~35% Gas turbine: ~40% Nuclear: ~33% Solar PV: ~15-20% Wind: ~35-45% Hydroelectric: ~85-90%

Thermodynamic limit from Carnot: Lower at lower temperature differences

Carbon Footprint​

Lowest during lifetime:

  • Nuclear
  • Wind
  • Hydroelectric

Higher:

  • Coal
  • Natural gas
  • Oil

Key Points​

  1. Light speed constant in all frames
  2. Time dilates at high speeds
  3. E = mc² shows mass-energy equivalence
  4. X-rays from electron deceleration
  5. Ultrasound uses reflection/Doppler
  6. Nuclear tracers show tissue activity
  7. Lasers produce coherent light
  8. Quarks and leptons fundamental
  9. Stars evolve through predictable cycle
  10. Renewable energy sustainable long-term

Practice Questions​

  1. Calculate relativistic effects
  2. Analyze X-ray imaging
  3. Interpret ultrasound images
  4. Describe particle interactions
  5. Apply Hertzsprung-Russell diagram
  6. Calculate solar/wind power
  7. Compare energy sources
  8. Analyze medical imaging
  9. Predict particle decays
  10. Evaluate sustainable options

Revision Tips​

  • Understand E = mc² concept
  • Know medical imaging principles
  • Learn particle types
  • Understand star lifecycle
  • Know renewable advantages/disadvantages
  • Practice relativistic calculations
  • Understand quantum concepts
  • Connect theory to applications
  • Consider sustainability
  • Stay current with developments