Atoms, nuclei and radiation

Setup. Alpha particles fired at thin gold foil. Detected on screen around foil.

Observations.

• Most passed straight through → atom mostly EMPTY space.
• A few deflected through large angles → concentrated +charge.
• Very few backscattered → nucleus has large mass.

Conclusion. Atom has tiny dense positively-charged NUCLEUS at centre; electrons orbit at relatively large distance.

Cambridge tip. Mark scheme rewards all three observations + conclusions.

Notation. $^A_Z \text{X}$.

• $Z$: proton number (atomic number).
• $A$: nucleon number (mass number) = $Z + N$.
• $N$: neutron number = $A - Z$.

Isotope. Same $Z$, different $N$. e.g. $^{12}_6 \text{C}$ and $^{14}_6 \text{C}$ (both carbon, different mass).

Element identity. Determined by $Z$ alone.

Cambridge tip. Mark scheme rewards clear $Z$, $A$, $N$ identification.

Alpha (α). Helium-4 nucleus. Charge $+2e$. Mass 4 u. Stopped by paper or a few cm of air. Most ionising. Discrete energy spectrum (single energies per decay).

Decay equation: $^A_Z X \to ^{A-4}_{Z-2} Y + {}^4_2 \text{He}$.

Beta-minus (β⁻). High-energy electron. Charge $-e$, negligible mass (~1/1800 u). Stopped by ~few mm aluminium. Less ionising than α.

Origin: a neutron transforms into a proton plus an electron plus an electron antineutrino: $n \to p + e^- + \overline{\nu}_e$ Decay equation: $^A_Z X \to {}^A_{Z+1} Y + {}^{\;0}_{-1} e + \overline{\nu}_e$.

Beta-plus (β⁺, positron). High-energy POSITRON — the antiparticle of the electron. Same mass as the electron, opposite charge $+e$.

Origin: a proton transforms into a neutron plus a positron plus an electron neutrino: $p \to n + e^+ + \nu_e$ Decay equation: $^A_Z X \to {}^A_{Z-1} Y + {}^{\;0}_{+1} e + \nu_e$.

Why (anti)neutrinos? β-particles emerge with a CONTINUOUS range of energies, unlike the discrete α energies. The remaining energy is carried away by the (anti)neutrino — almost massless, neutral, very weakly interacting. This is also why energy AND momentum conservation hold even when only the β-particle is measured.

Gamma (γ). High-frequency EM wave. No mass, no charge. Stopped by several cm of lead. Least ionising. Often follows α/β decay as the daughter nucleus de-excites.

Comparison.

Property	α	β⁻	β⁺	γ
Identity	He-4 nucleus	electron	positron	EM wave (photon)
Charge	$+2e$	$-e$	$+e$	0
Mass	4 u	$\sim$ 1/1800 u	$\sim$ 1/1800 u	0
Spectrum	discrete	continuous	continuous	line/quasi-line
Ionising	very high	medium	medium	low
Penetration	low (paper)	medium (Al)	medium (Al)	high (Pb)
Always accompanied by	—	$\overline{\nu}_e$	$\nu_e$	—

Cambridge tip. Examiners want both β⁻ AND β⁺, plus the matching (anti)neutrino, plus the reason for the continuous spectrum — these three items together earn the marks reliably.

Antiparticle. For every particle there exists an antiparticle with the SAME MASS but OPPOSITE CHARGE (and opposite values of other additive quantum numbers). When a particle meets its antiparticle, they annihilate into photons.

Familiar antiparticles.

• Electron $e^-$ ↔ positron $e^+$ (used in PET imaging).
• Proton $p$ ↔ antiproton $\bar p$.
• Quark $q$ ↔ antiquark $\bar q$.
• (Neutrinos similarly: $\nu_e \leftrightarrow \overline{\nu}_e$.)

Unified atomic mass unit (u). A practical mass unit for nuclear physics. $1\,\text{u} = \frac{1}{12} m\left(^{12}\text{C atom}\right) \approx 1.661 \times 10^{-27}\,\text{kg}$

By $E = mc^2$: $1\,\text{u} \leftrightarrow 931.5\,\text{MeV}$ — the conversion you'll use for mass defect calculations later in this topic.

Cambridge tip. Always state the definition of u with reference to $^{12}$C — examiners look for that exact wording.