Radioactive decay modes — α, β⁻, β⁺, electron capture, γ, spontaneous fission

5.2.2 · Chemistry › Nuclear & Radiochemistry

WHY yeh hota hai: Bahut heavy nuclei mein bahut saare protons ke beech ki repulsion strong nuclear force se zyada ho jaati hai. Ek tightly-bound α cluster ko nikalna total energy ko kam karta hai. α particle special hai kyunki $_{2}^{4} He$ ki binding energy per nucleon unusually high hoti hai — ise thookna energetically "sasta" hai.

HOW numbers change hote hain: $A$ 4 se ghatta hai, $Z$ 2 se ghatta hai.

2. Beta-minus (β⁻) decay

WHY: Nucleus neutron-rich hai (valley of stability ke neeche). Ek neutron ko proton mein convert karna use stability ki taraf le jaata hai. Electron decay ke waqt create hota hai — woh nucleus ke andar nahi baitha tha.

HOW numbers change hote hain: $A$ unchanged, $Z$ 1 se badhta hai.

3. Beta-plus (β⁺) decay (positron emission)

WHY: Nucleus proton-rich hai (valley ke upar). Ise kam protons chahiye.

HOW: $A$ unchanged, $Z$ 1 se ghatta hai.

4. Electron capture (EC)

WHY yeh β⁺ se compete karta hai: Dono ek proton-rich nucleus ko fix karte hain ( $Z \to Z - 1$ ). Lekin EC ka $2 m_{e} c^{2}$ threshold nahi hota — sirf $Q > 0$ chahiye. Toh jab atomic mass difference 1.022 MeV se kam hota hai, EC ek akeela available channel hota hai; usse upar, dono compete karte hain.

HOW tum EC ko pehchaante ho: Koi charged particle emit nahi hota, lekin inner shell mein jo vacancy banti hai woh ek outer electron se bhar jaati hai → characteristic X-ray emit hoti hai (experimental fingerprint yahi hai).

5. Gamma (γ) emission

WHY: α/β decay ke baad daughter aksar ek excited nuclear level mein "vibrate" karti rehti hai. Jaise ek electron orbitals drop karta hai, nucleus photon emit karke de-excite hota hai — lekin nuclear energy gaps MeV-scale ke hote hain (electrons ke liye eV ke muqable), isliye γ-rays bante hain na ki visible light.

6. Spontaneous fission (SF)

WHY: Super-heavy nuclei ( $A ≳ 250$ ) mein Coulomb repulsion itni strong hoti hai ki nucleus deform hokar do medium nuclei mein toot sakta hai, jinmein se har ek ki binding energy per nucleon zyada hoti hai → bahut badi energy release hoti hai. Yeh α decay se compete karta hai; Cf, Fm jaise elements ke liye dominant ho jaata hai.

Figure — Radioactive decay modes — α, β⁻, β⁺, electron capture, γ, spontaneous fission

Summary table (80/20 core)

Mode	Emitted	$Δ Z$	$Δ A$	Fixes
α	$_{2}^{4} He$	$- 2$	$- 4$	bahut heavy
β⁻	$e^{-} + \overset{ν}{ˉ}_{e}$	$+ 1$	$0$	neutron-rich
β⁺	$e^{+} + ν_{e}$	$- 1$	$0$	proton-rich (>1.022 MeV chahiye)
EC	$ν_{e}$ (+ X-ray)	$- 1$	$0$	proton-rich (koi bhi $Q > 0$ )
γ	photon	$0$	$0$	excited state
SF	fragments + $n$	varies	varies	super-heavy

Common mistakes (Steel-man + fix)

Flashcards

α decay kaun si problem solve karta hai?

Ek nucleus jo bahut heavy hai (bahut bada

A

/bahut zyada Coulomb repulsion).

General α decay equation likho.

_{Z}^{A} X \to_{Z - 2}^{A - 4} Y +_{2}^{4} He

β⁻ decay mein nucleus ke andar kya kya mein transform hota hai?

Neutron → proton + electron + antineutrino.

β⁻ decay mein

Z

aur

A

kaise change hote hain?

Z

1 se badhta hai;

A

unchanged.

β decay mein antineutrino kyun emit hota hai?

Energy/momentum conserve karne ke liye — continuous β energy spectrum explain karta hai.

β⁺ decay mein kya transform hota hai aur

Z

kaise change hota hai?

Proton → neutron + positron + neutrino;

Z

1 se ghatta hai.

β⁺ decay ko ≥ 1.022 MeV kyun chahiye?

Ek positron create karne aur atomic-mass bookkeeping mein

2 m_{e} c^{2} = 1.022

MeV lagti hai.

Electron capture β⁺ se kaise alag hai?

EC ek inner electron absorb karta hai (koi positron nahi, koi 1.022 MeV threshold nahi) aur ek characteristic X-ray emit karta hai.

Electron capture ka experimental fingerprint kya hai?

Inner-shell vacancy bharne se characteristic X-ray.

γ emission mein kya change hota hai?

A

Z

mein kuch nahi — sirf energy (excited → ground state, photon release hota hai).

Spontaneous fission kya hai aur kab dominant hota hai?

Ek heavy nucleus do medium fragments + free neutrons mein toot jaata hai; super-heavy nuclei (

A ≳ 250

) ke liye dominant hota hai.

α decay ka Q-value formula kya hai?

Q = [m (X) - m (Y) - m (α)] c^{2}

, atomic masses use karke (electrons cancel ho jaate hain).

Kaun sa decay ek neutron-rich nucleus ko stability ki taraf le jaata hai?

β⁻ (

N ↓

Z ↑

Recall Feynman: 12-saal ke bachche ko samjhao

Ek unstable nucleus settle hone ki koshish karte ek hilaate hue blocks ke tower jaisi hai. Agar tower bahut tall hai (bahut heavy), toh woh 2-red-2-blue blocks ka ek tukda phenkti hai (α). Agar usme bahut zyada blue blocks (neutrons) hain, toh ek blue block red mein flip ho jaata hai aur ek chhota electron bahar nikalata hai (β⁻). Agar usme bahut zyada red blocks (protons) hain, toh ek red blue mein flip hota hai — ya toh ek positron thookkar (β⁺) ya ek passing electron pakad kar (EC). Agar tower sahi shape mein hai par abhi bhi hilti hai, toh woh sirf ek flash of light deti hai (γ). Aur ek bahut bada tower sirf do hisson mein toot jaata hai (fission). Har move tower ko aur zyada stable banata hai.

Connections

Valley of Stability and N-Z ratio
Binding Energy per Nucleon
Half-life and First-order Decay Kinetics
Nuclear Reactions and Q-value
Mass-Energy Equivalence E=mc²
Carbon-14 Dating
Nuclear Fission and Chain Reactions
Characteristic X-rays and Electron Shells