Radioactive decay — alpha, beta, gamma — mechanisms
1. The master rule: conservation laws
Every decay must conserve:
- Charge (atomic number on both sides).
- Nucleon number (mass number on both sides).
- Energy–momentum (this gives the Q-value and the kinetic energies).
- Lepton number (this is why neutrinos exist — keep reading).
2. Alpha decay
WHY an alpha and not, say, a single proton? Because is exceptionally tightly bound (binding energy per nucleon ≈ 7.07 MeV). Ejecting it as a pre-formed, low-mass, high-binding clump makes positive for heavy nuclei where a single nucleon could not escape.
HOW it physically happens — quantum tunnelling: Inside the nucleus, an alpha cluster is trapped behind the Coulomb barrier (the wall of electrostatic repulsion). Classically it has too little energy to climb out. But quantum mechanics gives a small probability to tunnel through the barrier. The thinner/lower the barrier, the faster the decay — this is the heart of the Geiger–Nuttall law (more energetic alphas → much shorter half-lives).
3. Beta decay
There are two flavours. Both change a neutron↔proton, keeping fixed but shifting .
WHY a neutrino must exist (the historic puzzle): Early experiments saw the emitted electron come out with a continuous range of energies up to a maximum, not a single line. If only were produced, two-body kinematics forces a fixed electron energy. The smooth spread meant a third, invisible particle shared the energy: Pauli's neutrino. It also rescues lepton-number and angular-momentum conservation.
4. Gamma decay
WHY: After an alpha or beta decay, the daughter often lands in an excited nuclear state, not the ground state. Just like an atom de-excites by emitting visible light, the nucleus de-excites by emitting a much higher-energy photon (keV–MeV) because nuclear energy gaps are huge.
5. Comparison table
| Property | Alpha | Beta | Gamma |
|---|---|---|---|
| Emitted | He nucleus | electron + | photon |
| Charge | |||
| Spectrum | discrete | continuous | discrete |
| Penetration | low (paper) | medium (Al sheet) | high (lead/concrete) |
| Mechanism | tunnelling | weak interaction | EM de-excitation |
Recall Feynman: explain to a 12-year-old
Imagine a wobbly tower of blocks that's too tall. To stop wobbling it can (1) throw off a small solid 4-block chunk — that's alpha; (2) flip one block from a "neutron" type to a "proton" type, spitting out a tiny electron and a ghost particle (neutrino) — that's beta; or (3) if it's still jiggling after the change, it shakes off the extra jiggle as a flash of invisible super-light — that's gamma. Every move makes the tower steadier (lower energy), and the leftover energy becomes motion.
Flashcards
What particle is emitted in alpha decay?
In decay, what happens at the nucleon level?
Why is the beta energy spectrum continuous, not discrete?
Why must a neutrino exist in beta decay?
What is the Q-value of a decay?
Why doesn't the alpha take 100% of Q?
Give the alpha kinetic-energy formula.
What is the mechanism of alpha emission?
How does gamma decay change A and Z?
What changes in decay?
Which radiation penetrates most / least?
Why is alpha favoured over single-proton emission for heavy nuclei?
Connections
- Nuclear binding energy and mass defect — why drives all decays.
- Quantum tunnelling — the engine behind alpha emission and Geiger–Nuttall.
- Weak interaction — the force responsible for beta decay.
- Law of radioactive decay (N = N0 e^-λt) — the rate once a mechanism exists.
- Neutrino and lepton number conservation — why beta needs a ghost particle.
- Nuclear energy levels and shell model — the levels behind gamma lines.
Concept Map
Hinglish (regional understanding)
Intuition Hinglish mein samjho
Dekho, radioactive decay ka basic funda simple hai: jo nucleus unstable hai, woh kisi tareeke se apni energy kam karke zyada stable banna chahta hai. Agar nucleus bahut bhaari hai (heavy, jaise Uranium), toh woh ek chhota tight chunk — He, yaani alpha particle — bahar phenk deta hai. Isse 2 se kam aur 4 se kam ho jaata hai. Yeh alpha quantum tunnelling se nikalta hai — Coulomb barrier ko classically cross nahi kar sakta, par quantum mechanics thodi probability deta hai.
Beta decay tab hota hai jab neutron–proton ka ratio galat hai. Agar neutrons zyada hain, ek neutron proton ban jaata hai aur ek electron + antineutrino nikal jaata hai (, ek se badh jaata hai). Important baat: yeh electron pehle se nucleus mein nahi tha — woh decay ke time banta hai. Aur kyunki yeh teen cheezein (daughter + electron + neutrino) energy aapas mein baant leti hain, electron ki energy ek fixed value nahi, balki continuous range hoti hai 0 se maximum (endpoint) tak. Isi continuous spectrum ne hi neutrino ke existence ko prove kiya tha.
Gamma decay mein aur kuch nahi badalte. Alpha ya beta ke baad daughter nucleus aksar excited state mein hota hai (extra jiggle), aur woh extra energy ek high-energy photon () ki form mein chhod deta hai — bilkul waise jaise atom light emit karta hai, par bahut zyada energy ke saath.
Yaad rakhne ka shortcut: alpha = ; beta-minus = ; gamma = kuch nahi badalta, sirf energy jaati hai. Aur har decay mein Q-value positive hona chahiye — tabhi decay hota hai, kyunki nature hamesha lower energy ki taraf rolls karti hai.