National Year 12 Physics
Chapters: 5
1. 3.1 Measurements and their errors
3.1.1 Use of SI units and their prefixes · 3.1.2 Limitation of physical measurements · 3.1.3 Estimation of physical quantities
- Units and Measurement (Class 11) – To measure means to compare a quantity with a fixed, agreed amount called a unit. Result = number × unit. The world now uses the SI system with 7 base units: metre, kilogram, second, ampere, kelvin, mole and candela. Every other unit (like newton or joule) is a derived unit made by multiplying or dividing base units. Prefixes like kilo (10³) and milli (10⁻³) make very big or very small numbers easy.
- Significant Figures and Errors in Measurement – No measurement is perfect. Significant figures are the digits we trust plus the first doubtful digit. Errors tell how far a reading may be from the true value: absolute error Δa, relative error Δa/a and percentage error (Δa/a) × 100. When we add or subtract, absolute errors add. When we multiply or divide, percentage errors add. For a power aⁿ, the percentage error becomes n times.
- Estimation and Order of Magnitude – An estimate is a quick, sensible answer made with rounded numbers. Count a small part, multiply up, and give the answer to a sensible precision. The order of magnitude is the nearest power of ten, such as 10² for about 100.
2. 3.2 Particles and radiation
3.2.1 Particles · 3.2.2 Electromagnetic radiation and quantum phenomena
- Nuclear Physics: the Nucleus and Radioactivity – The nucleus holds protons (Z) and neutrons (N); mass number A = Z + N. Isotopes have the same Z but different N. Unstable nuclei decay at random: alpha decay removes 2 protons and 2 neutrons (A − 4, Z − 2), beta-minus decay turns a neutron into a proton and an electron (Z + 1), and gamma is energy only. Half-life is the time for half the nuclei in a sample to decay.
- Photoelectric Effect and Einstein's Equation – When light of high enough frequency falls on a metal, electrons jump out at once. Light comes in packets called photons, each with energy E = hν. One photon gives all its energy to one electron: hν = φ + KEmax, where φ is the work function. Below the threshold frequency ν₀ = φ/h no electron comes out, however bright the light.
3. 3.3 Waves
3.3.1 Progressive and stationary waves · 3.3.2 Refraction, diffraction and interference
- Progressive Waves: Types, Speed and Equation – A wave carries energy from place to place without carrying the matter along. In a transverse wave the particles move at right angles to the wave; in a longitudinal wave they move along it. Speed v = fλ. On a string v = √(T/μ); for sound in a gas v = √(γP/ρ). A wave moving along +x is y = A sin(kx − ωt), with k = 2π/λ and ω = 2πf.
- Interference (Young's Double Slit) and Single Slit Diffraction – Two coherent sources (same frequency, fixed phase difference) make a steady pattern of bright and dark fringes. At a point on the screen the path difference is Δ = yd/D: bright where Δ = nλ, dark where Δ = (n + ½)λ. All fringes have equal width β = λD/d. A single slit of width a gives diffraction: a bright central maximum of width 2λD/a, with first minima where a sin θ = λ, and weaker side maxima.
4. 3.4 Mechanics and materials
3.4.1 Force, energy and momentum · 3.4.2 Materials
- Inertia, First Law, Momentum, Second Law and Impulse – A body keeps its state of rest or uniform motion unless a net external force acts on it (first law). Inertia is this laziness to change, and mass measures it. Momentum p = mv. The rate of change of momentum equals the net force: F = dp/dt, which gives F = ma when mass is constant (second law). Impulse J = F × Δt = Δp; a longer stopping time means a smaller force.
- Mechanical Properties of Solids: Stress, Strain and Elasticity – When you pull, push or twist a solid, it changes shape a little. If it comes back when you let go, it is elastic. Stress is the restoring force per area (F/A). Strain is the fractional change in size (like ΔL/L). Up to the elastic limit, stress is proportional to strain (Hooke's law), and the ratio is a modulus: Young's modulus Y for stretching, bulk modulus B for squeezing all round, shear modulus G for sliding faces. A stretched wire also gets thinner (Poisson's ratio), and it stores energy ½ × stress × strain × volume.
5. 3.5 Electricity
3.5.1 Current electricity
- Ohm's Law, Resistivity and Effect of Temperature – Using drift velocity, V = IR with R = ml/(ne²τA) = ρl/A. Resistivity ρ = m/(ne²τ) depends only on the material and temperature; conductivity σ = 1/ρ. Ohm's law in vector form is j = σE. Metals, wires and resistors give a straight V–I line (ohmic); bulbs, diodes and devices like GaAs give curved or one-way graphs (non-ohmic). For metals ρ rises with temperature: ρT = ρ0[1 + α(T − T0)]; alloys like nichrome change very little; semiconductors get lower ρ when hot.