Romania Clasa a XII-a Physics (F1)

Chapters: 5

1. Special relativity

Foundations · Relativistic kinematics and dynamics

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.

External photoelectric effect · *Compton effect · De Broglie waves

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.
Matter Waves and the de Broglie Relation – Light behaves like a wave and a particle. In 1924 Louis de Broglie said matter does the same: every moving particle has a wave with wavelength λ = h/p = h/mv. For a body of kinetic energy K, λ = h/√(2mK); for an electron accelerated through V volts, λ = 1.227/√V nm. Everyday objects have far too tiny a λ to notice, but electrons have λ about the size of atoms.

Atomic models and spectra · X-rays and lasers

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.
Lasers: How Stimulated Emission Makes a Beam of Light – LASER stands for Light Amplification by Stimulated Emission of Radiation. A pump lifts atoms to a higher energy level. When a photon of the right energy passes an excited atom, the atom gives out a second, identical photon. With more atoms excited than unexcited (population inversion) and mirrors at each end, the light builds up into a narrow, single-colour, coherent beam. X-rays are also high-energy light, made when fast electrons hit a metal target.

Semiconductor devices

Semiconductors and the p-n Junction Diode – A semiconductor has a small energy gap (about 1 eV), so a little heat frees some electrons. Pure silicon is intrinsic (electrons = holes). Adding a 5-valence atom makes n-type; a 3-valence atom makes p-type. Joining p and n makes a junction with a depletion layer and a barrier (about 0.7 V for Si). The diode conducts in forward bias, almost not in reverse bias, so it can change AC into one-way DC (rectifier).

The nucleus · Fission and fusion · *Accelerators and elementary particles

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).
Particle Physics: Quarks, Leptons and the Standard Model – Particle physics studies the smallest building blocks of matter. Protons and neutrons are made of quarks. Electrons belong to a family called leptons. Every particle has an antiparticle. Particles feel four forces, and three of them are carried by messenger particles called bosons. All of this together is called the Standard Model.