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Theme E · Nuclear & Quantum Physics

Chapter 2 · Nuclear processes

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Radioactive decay law
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
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
E=mc2E = mc^2
c=3.0×108c = 3.0\times10^8 m/s.
Binding energy
Energy to split a nucleus into nucleons. Higher binding energy per nucleon = more stable (peak near iron-56).
Fission vs fusion
Fission: heavy nucleus splits. Fusion: light nuclei merge (powers stars). Both release energy via mass defect.
Photon energy
E=hf=hcλE = hf = \frac{hc}{\lambda}
h=6.63×10−34h = 6.63\times10^{-34} J s.
Photoelectric effect
Ek,max⁡=hf−ϕE_{k,\max} = hf - \phi
No emission below threshold frequency, however bright.
Stopping potential
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
λ=hp=hmv\lambda = \frac{h}{p} = \frac{h}{mv}
Particles have wave nature; tiny for macroscopic objects.
Decay equations balance
Conserve nucleon number AA and proton number ZZ on both sides. α: emit 24He{}^4_2\text{He}; β⁻: a neutron → proton + electron.
Activity
A=λNA = \lambda N
Decays per second, becquerel (Bq); λ\lambda = decay constant (s⁻¹), not wavelength here.
Mass defect → energy
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
Nuclei must overcome Coulomb repulsion to get close enough for the strong force — needs huge KE (temperature).
Photoelectric — key idea
One photon, one electron. Below threshold f, NO emission however intense; above, brighter = more electrons (same max KE).
Key SI units
T1/2T_{1/2}: s · λ\lambda (decay const): s⁻¹ · AA: Bq · EE: J (or MeV) · mm: kg (or u).
Common traps
Confusing decay constant λ with wavelength; not balancing A and Z; forgetting half-life is statistical (large samples).