Radioactive decay — alpha, beta, gamma — mechanisms

2.3.21 · Physics › Modern Physics

1. The master rule: conservation laws

Har decay mein ye conserve hone chahiye:

Charge (dono sides par atomic number $Z$ ).
Nucleon number (dono sides par mass number $A$ ).
Energy–momentum (isse Q-value aur kinetic energies milti hain).
Lepton number (isliye neutrinos exist karte hain — aage padho).

2. Alpha decay

ALPHA KYUN, aur maan lo ek single proton kyun nahi? Kyunki $_{2}^{4} He$ exceptionally tightly bound hoti hai (binding energy per nucleon ≈ 7.07 MeV). Isse ek pre-formed, low-mass, high-binding clump ki tarah eject karna heavy nuclei ke liye $Q$ ko positive banaata hai jahan ek single nucleon escape nahi kar sakta.

YE PHYSICALLY KAISE HOTA HAI — quantum tunnelling: Nucleus ke andar, ek alpha cluster Coulomb barrier (electrostatic repulsion ki diwar) ke peeche trapped hota hai. Classically uske paas bahar niklne ke liye itni energy nahi hoti. Lekin quantum mechanics barrier ke through tunnel karne ki ek choti probability deta hai. Barrier jitni patli/neechi hogi, decay utni jaldi hogi — yahi Geiger–Nuttall law ki core baat hai (zyada energetic alphas → bahut chote half-lives).

3. Beta decay

Do flavours hote hain. Dono ek neutron↔proton change karte hain, $A$ fixed rakhte hain lekin $Z$ shift karte hain.

NEUTRINO KA EXIST KARNA KYUN ZAROORI HAI (ek historic puzzle): Early experiments mein dekha gaya ki emitted electron ek continuous range of energies ke saath bahar aata tha ek maximum tak, single line nahi. Agar sirf $Y + e^{-}$ produce hote, to two-body kinematics ek fixed electron energy force karta. Ye smooth spread ka matlab tha ki ek teesra, invisible particle energy share kar raha tha: Pauli ka neutrino. Isse lepton-number aur angular-momentum conservation bhi bachti hai.

4. Gamma decay

KYUN: Alpha ya beta decay ke baad, daughter aksar ek excited nuclear state mein land karti hai, ground state mein nahi. Jaise ek atom visible light emit karke de-excite hota hai, waise hi nucleus ek bahut zyada high-energy photon (keV–MeV) emit karke de-excite hota hai kyunki nuclear energy gaps bahut bade hote hain.

Figure — Radioactive decay — alpha, beta, gamma — mechanisms

5. Comparison table

Property	Alpha $α$	Beta $β^{-}$	Gamma $γ$
Emitted	$_{2}^{4}$ He nucleus	electron + $\overset{ν}{ˉ}_{e}$	photon
Charge	$+ 2 e$	$- e$	$0$
$Δ A$	$- 4$	$0$	$0$
$Δ Z$	$- 2$	$+ 1$	$0$
Spectrum	discrete	continuous	discrete
Penetration	kam (paper)	medium (Al sheet)	zyada (lead/concrete)
Mechanism	tunnelling	weak interaction	EM de-excitation

Common mistake Steel-manned mistakes

"Beta electrons orbital cloud se aate hain." Sahi lagta hai kyunki symbol electron hai aur atoms mein electrons hote hain. Fix: electron nucleus ke andar create hota hai jab $n \to p + e^{-} + \overset{ν}{ˉ}_{e}$ hota hai — pehle se nucleus mein koi electrons nahi baithe hote.

"Alpha saara Q-value le leta hai." Sahi lagta hai kyunki almost saara hota hi hai. Fix: momentum conservation daughter nucleus ko recoil karne aur ek chota share lene par majboor karta hai; $K E_{α} = Q \frac{m _{Y}}{m _{Y} + m _{α}}$ , $Q$ nahi.

"Beta ko alpha jaisi single energy deni chahiye." Sahi lagta hai analogy se. Fix: beta ek three-body decay hai (daughter + electron + neutrino), isliye energy continuously share hoti hai → spectrum, line nahi. Isi ne neutrino ki discovery ko force kiya.

"Gamma element badal deta hai." Sahi lagta hai — "ek aur decay." Fix: $γ$ sirf energy shed karta hai; $A$ aur $Z$ unchanged rehte hain, same element, same isotope.

Recall Feynman: ek 12-saal ke bache ko samjhao

Socho blocks ka ek hilta hua tower jo bahut lamba hai. Hilna band karne ke liye ye (1) ek chota solid 4-block chunk fek sakta hai — ye alpha hai; (2) ek block ko "neutron" type se "proton" type mein flip kar sakta hai, ek tiny electron aur ek ghost particle (neutrino) bahar nikalte hue — ye beta hai; ya (3) agar change ke baad bhi hilta raha, to extra hilne ko ek invisible super-light ki flash ke roop mein shake off karta hai — ye gamma hai. Har move tower ko zyada stable banata hai (lower energy), aur bacha hua energy motion ban jaata hai.

Flashcards

Alpha decay mein kaunsa particle emit hota hai?

_{2}^{4}

He nucleus (2 protons + 2 neutrons).

β^{-}

decay mein nucleon level par kya hota hai?

n \to p + e^{-} + \overset{ν}{ˉ}_{e}

;

Z \to Z + 1

A

unchanged.

Beta energy spectrum continuous kyun hoti hai, discrete kyun nahi?

Ye ek three-body decay hai; antineutrino electron ke saath released energy continuously share karta hai.

Beta decay mein neutrino ka exist karna kyun zaroori hai?

Observed continuous electron spectrum ko dekh kar energy, momentum, angular momentum aur lepton number conserve karne ke liye.

Kisi decay ka Q-value kya hota hai?

Q = (m_{parent} - m_{products}) c^{2}

; decay spontaneous tabhi hoti hai jab

Q > 0

Alpha 100% Q kyun nahi leta?

Momentum conservation daughter nucleus ko recoil karne aur ek chota kinetic share carry karne par majboor karta hai.

Alpha kinetic-energy formula do.

K E_{α} = Q m_{Y} / (m_{Y} + m_{α}) \approx Q (A - 4) / A

Alpha emission ka mechanism kya hai?

Ek pre-formed alpha cluster ka Coulomb barrier ke through quantum tunnelling.

Gamma decay

A

aur

Z

ko kaise change karta hai?

Kuch nahi change karta; sirf energy ek excited nucleus se photon ke roop mein release hoti hai.

β^{+}

decay mein kya change hota hai?

p \to n + e^{+} + ν_{e}

;

Z \to Z - 1

A

unchanged.

Kaun si radiation sabse zyada / sabse kam penetrate karti hai?

Gamma sabse zyada penetrate karti hai (lead chahiye); alpha sabse kam (paper rok leta hai).

Heavy nuclei ke liye single-proton emission ki jagah alpha kyun prefer hota hai?

^{4}

He bahut tightly bound hai, jo Q-value ko positive banata hai jahan single-nucleon emission possible nahi hota.

Connections

Nuclear binding energy and mass defect — kyun $Q > 0$ saari decays drive karta hai.
Quantum tunnelling — alpha emission aur Geiger–Nuttall ke peeche ka engine.
Weak interaction — wo force jo beta decay ke liye responsible hai.
Law of radioactive decay (N = N0 e^-λt) — rate jab koi mechanism exist karta hai.
Neutrino and lepton number conservation — beta ko ghost particle kyun chahiye.
Nuclear energy levels and shell model — gamma lines ke peeche ke levels.