Lower Saxony Zentralabitur Physics flashcards

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Zentralabitur kinematics equation

For constant acceleration the velocity is v = v₀ + a·t and the displacement is s = v₀·t + ½a·t². Eliminating time gives v² = v₀² + 2a·s. Free fall uses a = g ≈ 9.81 m/s².

Momentum conservation

In any collision or explosion with no external net force the total momentum p = Σm·v is constant. Kinetic energy is conserved only for elastic collisions, so momentum alone decides post-collision velocities.

Centripetal force

For circular motion of radius r at speed v the acceleration is a_z = v²/r directed toward the centre, so the required net force is F_z = m·v²/r. It changes direction, not speed.

Kepler's third law

For orbits around one central mass M, T²/r³ = 4π²/(G·M) is the same for all satellites. It follows from equating gravitational and centripetal force and allows determining M from orbital data.

Coulomb's law

Two point charges q₁ and q₂ at distance r exert forces F = (1/4πε₀)·|q₁q₂|/r² along the connecting line. With 1/4πε₀ = 8.99·10⁹ N·m²/C², equal signs repel and opposite signs attract.

Kirchhoff's rules

The node rule ΣI = 0 expresses charge conservation at a junction. The mesh rule ΣU = 0 expresses energy conservation around a closed loop. Together they solve multi-loop circuits with several sources.

Lorentz force on moving charge

A charge q moving with velocity v in a magnetic field B experiences F = q·v×B. The force is perpendicular to v, so it does no work and produces circular motion of radius r = m·v/(q·B).

Law of induction

A changing magnetic flux Φ = B·A·cos φ through a coil of N turns induces U_ind = −N·dΦ/dt. The minus sign is Lenz's law: the induced current opposes the change that produced it.

Harmonic oscillator period

A spring-mass system obeys F = −D·s and oscillates with T = 2π·√(m/D). A pendulum of length l gives T = 2π·√(l/g) for small amplitudes. Both are independent of amplitude.

Double-slit interference condition

Two coherent sources separated by d produce maxima at path difference Δs = n·λ and minima at Δs = (n + ½)·λ. For a screen distance a, the position follows from sin α ≈ d_n/a.

Diffraction grating equation

For a grating with slit spacing d, maxima appear at d·sin α_n = n·λ. Measuring the angle α_n for a known order n gives the wavelength λ = d·sin α_n/n.

Doppler effect for sound

A source approaching at speed v emits a compressed wavelength, so the observer hears f' = f·c/(c − v). Receding motion gives f' = f·c/(c + v). The effect requires relative motion.

Photoelectric equation

Light of frequency f ejects electrons with maximum kinetic energy E_kin = h·f − W_A, where W_A is the material's work function. Below the threshold f_G = W_A/h no electrons are emitted at all.

Photon energy

A photon carries E = h·f = h·c/λ with h = 6.626·10⁻³⁴ J·s. Using h·c = 1240 eV·nm makes quick conversion possible, e.g. 620 nm corresponds to about 2.0 eV.

de Broglie wavelength

Every particle with momentum p has an associated wavelength λ = h/p = h/(m·v). For electrons accelerated through voltage U this becomes λ = h/√(2·m_e·e·U), typically in the picometre range.

Bohr model energy levels

Hydrogen levels are E_n = −13.6 eV/n², with the ground state at −13.6 eV. A transition emits or absorbs a photon of energy h·f = |E_n − E_m|, producing the line spectrum.

Heisenberg uncertainty principle

Position and momentum cannot both be sharply defined: Δx·Δp ≥ h/(4π). This is a property of quantum states, not a limitation of measuring instruments, and explains natural line broadening.

Alpha and beta decay

Alpha decay emits a helium nucleus, lowering A by 4 and Z by 2. Beta-minus decay converts a neutron into a proton, raising Z by 1 while A stays constant, and emits an electron and antineutrino.

Radioactive decay law

The number of undecayed nuclei falls as N(t) = N₀·e^(−λt), with activity A = λ·N measured in becquerel. After n half-lives T₁/₂ = ln2/λ, the fraction (½)ⁿ remains.

Mass defect and binding energy

A nucleus is lighter than its separated nucleons by Δm. The binding energy E_B = Δm·c², often in MeV using 1 u = 931.5 MeV/c², measures nuclear stability and peaks near iron.

Mass-energy equivalence

Mass and energy are related by E = m·c². In nuclear reactions the mass difference between reactants and products appears as kinetic energy Q, which is why fusion and fission release energy.

Ideal gas law

For an ideal gas p·V = n·R·T with R = 8.314 J/(mol·K), or p·V = N·k_B·T. It links pressure, volume and absolute temperature and underlies isothermal, isobaric and isochoric processes.

First law of thermodynamics

The internal energy changes by ΔU = Q + W, where Q is heat supplied to the system and W is work done on it. For work done by the gas the form ΔU = Q − p·ΔV applies.

Carnot efficiency

No heat engine between reservoirs at T_hot and T_cold can exceed η_C = 1 − T_cold/T_hot, with temperatures in kelvin. Real engines fall short because of friction and irreversible heat transfer.

Entropy and second law

For a reversible process the entropy change is ΔS = Q_rev/T. The entropy of an isolated system never decreases, which defines the direction of spontaneous processes and forbids a perfect heat engine.

Lorentz factor

The factor γ = 1/√(1 − v²/c²) quantifies relativistic effects. It is about 1 for everyday speeds, reaches 1.15 at 0.5c and grows without bound as v approaches the speed of light.

Time dilation

A clock moving at speed v relative to an observer runs slow: Δt = γ·Δt₀, where Δt₀ is the proper time measured in the clock's rest frame. The effect is symmetric between inertial frames.

Length contraction

An object of proper length l₀ measured in its rest frame appears shortened to l = l₀/γ when moving at speed v. Contraction occurs only along the direction of relative motion, never perpendicular to it.

Relativistic energy-momentum relation

Total energy satisfies E² = (p·c)² + (m·c²)², with E = γ·m·c² and p = γ·m·v. For massless photons this reduces to E = p·c, linking momentum and energy without mass.

Error propagation in sums

For addition or subtraction the absolute uncertainties add: Δ(a ± b) = Δa + Δb. For multiplication and division the relative uncertainties add: Δ(ab)/(ab) = Δa/a + Δb/b.

Linearisation of data

Transforming an equation into y = m·x + b form allows a straight-line fit. For a pendulum, plotting T² against l gives slope 4π²/g, so the constant follows from the slope with its uncertainty.

Systematic versus random error

Random errors scatter in both directions and shrink when averaged over many trials. Systematic errors shift all readings the same way, for example a zero offset, and averaging does not remove them.