WHY this happens: For very heavy nuclei the repulsion between many protons outweighs the strong nuclear force. Ejecting a tightly-bound α cluster lowers the total energy. The α particle is special because 24He has an unusually high binding energy per nucleon — it's energetically "cheap" to spit out.
HOW the numbers change:A drops by 4, Z drops by 2.
WHY: The nucleus is neutron-rich (below the valley of stability). Converting a neutron to a proton moves it toward stability. The electron is created at the moment of decay — it was not sitting inside the nucleus.
HOW the numbers change:A unchanged, Zincreases by 1.
WHY this competes with β⁺: Both fix a proton-rich nucleus (Z→Z−1). But EC has no 2mec2 threshold — it only needs Q>0. So when the atomic mass difference is less than 1.022 MeV, EC is the only available channel; above it, both compete.
HOW you spot EC: No charged particle is emitted, but the vacancy left in the inner shell is filled by an outer electron → emission of a characteristic X-ray (the experimental fingerprint).
WHY: After α/β decay the daughter is often left "vibrating" in an excited nuclear level. Like an electron dropping orbitals, the nucleus de-excites by emitting a photon — but nuclear energy gaps are MeV-scale (vs eV for electrons), hence γ-rays not visible light.
WHY: For super-heavy nuclei (A≳250) Coulomb repulsion is so strong that the nucleus can deform and break into two medium nuclei, each with higher binding energy per nucleon → huge energy release. It competes with α decay; it dominates for elements like Cf, Fm.
A nucleus that is too heavy (too large A/too much Coulomb repulsion).
Write the general α decay equation.
ZAX→Z−2A−4Y+24He.
In β⁻ decay, what transforms into what inside the nucleus?
A neutron → proton + electron + antineutrino.
How do Z and A change in β⁻ decay?
Z increases by 1; A unchanged.
Why is an antineutrino emitted in β decay?
To conserve energy/momentum — explains the continuous β energy spectrum.
What transforms in β⁺ decay and how does Z change?
Proton → neutron + positron + neutrino; Z decreases by 1.
Why does β⁺ decay require ≥ 1.022 MeV?
Creating a positron plus the atomic-mass bookkeeping costs 2mec2=1.022 MeV.
How does electron capture differ from β⁺?
EC absorbs an inner electron (no positron, no 1.022 MeV threshold) and emits a characteristic X-ray.
Experimental fingerprint of electron capture?
Characteristic X-ray from the inner-shell vacancy being filled.
What changes in γ emission?
Nothing in A or Z — only energy (excited → ground state, photon released).
What is spontaneous fission and when does it dominate?
A heavy nucleus splits into two medium fragments + free neutrons; dominates for super-heavy nuclei (A≳250).
Q-value formula for α decay?
Q=[m(X)−m(Y)−m(α)]c2, using atomic masses (electrons cancel).
Which decay moves a neutron-rich nucleus toward stability?
β⁻ (N↓, Z↑).
Recall Feynman: explain it to a 12-year-old
An unstable nucleus is like a wobbly tower of blocks trying to settle. If the tower is too tall (too heavy) it tosses off a chunk of 2-red-2-blue blocks (α). If it has too many blue blocks (neutrons), one blue block flips into a red one and shoots out a tiny electron (β⁻). If it has too many red blocks (protons), a red flips into blue — either by spitting out a positron (β⁺) or by grabbing a passing electron (EC). If the tower is the right shape but still jiggling, it just lets out a flash of light (γ). And a gigantic tower simply breaks in half (fission). Each move makes the tower steadier.
Dekho, har radioactive nucleus basically unstable hai — uska neutron-to-proton ratio galat hai ya usme extra energy hai. Decay ka matlab hai nucleus ko "valley of stability" ki taraf le jaana, jahan woh sabse stable rehta hai. Har decay mode ek specific problem ka solution hai. Agar nucleus bahut bhaari hai, toh woh ek alpha particle (24He, 2 proton + 2 neutron) phenk deta hai — A 4 se kam, Z 2 se kam.
Agar nucleus me neutron zyada hain (neutron-rich), toh ek neutron proton ban jaata hai aur ek electron + antineutrino nikalta hai — yeh β⁻ decay hai, jisme Z 1 se badhta hai par A same. Yaad rakho electron A=0 hai, isliye mass number nahi badalta. Ulta agar proton zyada hain, toh proton neutron banta hai — ya β⁺ (positron niklta hai, par iske liye 1.022 MeV energy chahiye) ya electron capture (nucleus apne andar ka electron nigal leta hai, koi threshold nahi, aur ek characteristic X-ray nikalti hai). Dono me Z 1 se ghatta hai.
γ decay me toh kuch transmute hota hi nahi — bas nucleus excited state se ground state me aata hai aur ek high-energy photon chhodta hai; A aur Z bilkul same. Aur spontaneous fission super-heavy nuclei (jaise Cf) me hota hai, jahan nucleus do tukdo me toot jaata hai plus kuch free neutrons. Trick yeh hai: har equation me A aur Z dono sides pe balance hone chahiye — yahi check tumhe har baar sahi answer dega.
