Poland Liceum ogólnokształcące, klasa IV Physics (extended level)
Chapters: 3
1. Waves and optics
Wave properties · Reflection, refraction and lenses · Diffraction, interference, Doppler, polarisation · Experiments: waves and optics
- 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.
- Thin Lenses: Lens Maker's Formula, Lens Formula and Power – At one curved surface, n₂/v − n₁/u = (n₂ − n₁)/R. Two such surfaces make a thin lens with 1/f = (n − 1)(1/R₁ − 1/R₂) (lens maker's formula). Object and image distances follow 1/v − 1/u = 1/f, magnification m = v/u, power P = 1/f (in dioptres when f is in metres), and thin lenses in contact add their powers: P = P₁ + P₂.
- 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.
2. Atomic physics
Photons and atoms
- Atoms: From Alpha Scattering to the Bohr Model – Rutherford shot alpha particles at thin gold foil and found that an atom is mostly empty, with a tiny, heavy, positive nucleus in the middle. Bohr then said the electron in hydrogen can move only on fixed orbits where its angular momentum is nh/2π. In orbit n the radius is 0.529 n² Å, the speed is (2.19 × 10⁶)/n m/s and the energy is −13.6/n² eV. When the electron jumps down, the energy difference comes out as light of one exact colour, which gives the line spectrum of hydrogen.
3. Relativity and nuclear physics
Elements of relativity · Nuclei and decay · Nuclear energy, stars and antimatter
- Special Relativity – Special relativity (Einstein, 1905) rests on two postulates: the laws of physics are the same in all inertial frames, and the speed of light in a vacuum, c ≈ 3.00 × 10⁸ m/s, is the same for every observer. It follows that moving clocks run slow (t = γt₀), moving objects are shorter along their motion (L = L₀/γ), and mass is a form of energy (E = mc²), with γ = 1/√(1 − v²/c²). At everyday speeds γ ≈ 1, so Newton's mechanics works; near c it fails.
- Radioactivity: Alpha, Beta, Gamma and Half-Life – Some atomic nuclei are unstable. They give out radiation at random to become more stable. This is radioactive decay. Alpha (2 protons + 2 neutrons), beta (a fast electron) and gamma (a wave of energy) are the three main kinds. Half-life is the time for half of the unstable nuclei to decay.
- Nuclei: Size, Nuclear Force, Binding Energy, Fission and Fusion – A nucleus is made of Z protons and N neutrons (A = Z + N nucleons). Its radius is R = R₀A^(1/3) with R₀ ≈ 1.2 fm, so every nucleus has almost the same huge density. A very strong, short-range nuclear force holds the nucleons together. The nucleus weighs a little less than its loose parts; this mass defect Δm is the binding energy, E = Δm c² (1 u = 931.5 MeV). Binding energy per nucleon is highest near iron (A ≈ 56), so heavy nuclei give energy when they split (fission) and light nuclei give energy when they join (fusion).