← Theme E · Nuclear & Quantum Physics
Physics · Topic Cheatsheet

Theme E · Nuclear & Quantum Physics

28 key results accumulated across 3 chapters.

Nuclear notation
Ch 1
ZAX{}^{A}_{Z}X
ZZ = protons, AA = nucleons, N=A−ZN = A - Z = neutrons.
Isotopes
Ch 1
Same ZZ, different NN — same element, different mass.
Neutral atom
Ch 1
electrons = protons = ZZ. An ion has electrons ≠ protons.
Three subatomic particles
Ch 1
Proton (+e, in nucleus), neutron (0, in nucleus), electron (−e, ≈1/1836\approx 1/1836 mass).
Energy levels
Ch 1
Electrons occupy discrete (quantised) energy levels around the nucleus.
Emission/absorption spectra
Ch 1
ΔE=hf\Delta E = hf
Electrons jumping levels emit/absorb photons of specific frequencies → line spectra.
Photon energy
Ch 1
E=hf=hcλE = hf = \frac{hc}{\lambda}
h=6.63×10−34h = 6.63\times10^{-34} J s; higher f ⇒ more energetic photon.
Electronvolt (energy unit)
Ch 1
1 eV=1.6×10−19 J1\,\text{eV} = 1.6\times10^{-19}\,\text{J}
Convenient for atomic/nuclear energies; multiply eV by e to get joules.
Strong nuclear force
Ch 1
Very short range, attractive — holds the nucleus together against proton–proton repulsion.
Evidence for the nucleus
Ch 1
Geiger–Marsden (gold foil): most α pass through ⇒ atom is mostly empty; few bounce back ⇒ tiny dense + nucleus.
Key SI units
Ch 1
EE: J (or eV) · ff: Hz · λ\lambda: m · Z,A,NZ,A,N: counts (no unit).
Common traps
Ch 1
Forgetting to convert eV→J before using SI formulas; mixing ZZ (protons) and AA (nucleons).
Radioactive decay law
Ch 2
N(t)=N0(12)t/T1/2N(t) = N_0\left(\tfrac{1}{2}\right)^{t/T_{1/2}}
After nn half-lives, N0/2nN_0/2^n remain.
Decay types
Ch 2
α\alpha (He nucleus, Z−2,A−4Z{-}2,A{-}4, stopped by paper); β−\beta^- (electron, Z+1Z{+}1, stopped by aluminium); γ\gamma (photon, no change, needs lead).
Mass–energy equivalence
Ch 2
E=mc2E = mc^2
c=3.0×108c = 3.0\times10^8 m/s.
Binding energy
Ch 2
Energy to split a nucleus into nucleons. Higher binding energy per nucleon = more stable (peak near iron-56).
Fission vs fusion
Ch 2
Fission: heavy nucleus splits. Fusion: light nuclei merge (powers stars). Both release energy via mass defect.
Photon energy
Ch 2
E=hf=hcλE = hf = \frac{hc}{\lambda}
h=6.63×10−34h = 6.63\times10^{-34} J s.
Photoelectric effect
Ch 2
Ek,max⁡=hf−ϕE_{k,\max} = hf - \phi
No emission below threshold frequency, however bright.
Stopping potential
Ch 2
Vs=he f−ϕeV_s = \dfrac{h}{e}\,f - \dfrac{\phi}{e}
The reverse voltage that just stops the most energetic photoelectrons. Plot VsV_s vs ff gives a line of gradient h/eh/e (universal) and y-intercept −ϕ/e-\phi/e (metal-dependent) — the IB Paper-3 canonical data question.
de Broglie wavelength
Ch 2
λ=hp=hmv\lambda = \frac{h}{p} = \frac{h}{mv}
Particles have wave nature; tiny for macroscopic objects.
Decay equations balance
Ch 2
Conserve nucleon number AA and proton number ZZ on both sides. α: emit 24He{}^4_2\text{He}; β⁻: a neutron → proton + electron.
Activity
Ch 2
A=λNA = \lambda N
Decays per second, becquerel (Bq); λ\lambda = decay constant (s⁻¹), not wavelength here.
Mass defect → energy
Ch 2
E=Δm c2E = \Delta m\,c^2
1 u=931.5 MeV/c21\,\text{u} = 931.5\,\text{MeV}/c^2; products are lighter than reactants.
Why fusion needs high T
Ch 2
Nuclei must overcome Coulomb repulsion to get close enough for the strong force — needs huge KE (temperature).
Photoelectric — key idea
Ch 2
One photon, one electron. Below threshold f, NO emission however intense; above, brighter = more electrons (same max KE).
Key SI units
Ch 2
T1/2T_{1/2}: s · λ\lambda (decay const): s⁻¹ · AA: Bq · EE: J (or MeV) · mm: kg (or u).
Common traps
Ch 2
Confusing decay constant λ with wavelength; not balancing A and Z; forgetting half-life is statistical (large samples).