Rutherford's gold-foil experiment — nuclear model

1.2.4 · Chemistry › Atomic Structure (Classical)

1. Setup — KIYA KYA GAYA tha actually

Figure — Rutherford's gold-foil experiment — nuclear model

2. Observations — KYA DEKHA gaya

3. Nuclear model derive karna — CONCLUSIONS kaise aate hain

3.1 Closest approach estimate karna (nucleus ka size)

Formula Distance of closest approach

$r_{0}$ — energy conservation se derive kiya Ek α-particle ko head-on fire karo. Woh slow hoti hai, distance $r_{0}$ par rukti hai, phir reverse hoti hai. Rukne ke point par saari kinetic energy electrostatic potential energy ban jaati hai.

Step 1 — Energy conservation kyun? Koi energy lost nahi hoti (elastic Coulomb interaction), isliye $KE_{initial} = PE at closest approach$ Step 2 — Dono sides likho. α ki KE $\frac{1}{2} m v^{2}$ hai. Charge $q_{1} = 2 e$ (α) aur $q_{2} = Z e$ (nucleus, gold ke liye $Z = 79$ ) ke beech Coulomb PE hai $U = \frac{1}{4 π ε _{0}} \frac{q _{1} q _{2}}{r} .$ Step 3 — Unhe $r = r_{0}$ par equal karo (jahan $v = 0$ ): $\frac{1}{2} m v^{2} = \frac{1}{4 π ε _{0}} \frac{( 2 e ) ( Z e )}{r _{0}} .$ Step 4 — $r_{0}$ ke liye solve karo: $r_{0} = \frac{1}{4 π ε _{0}} \frac{2 Z e ^{2}}{\frac{1}{2} m v ^{2}} = \frac{1}{4 π ε _{0}} \frac{4 Z e ^{2}}{m v ^{2}}$ Gold mein plug karne par $r_{0} \sim 1 0^{- 14}$ m milta hai — atom ( $\sim 1 0^{- 10}$ m) se hazaaron guna chhhota. Yeh size gap hi nuclear model hai.

4. Rutherford's nuclear model — KYA KEHTA HAI yeh

5. Model ki failures — Classical picture ko steel-man karna

Common mistake "Ek revolving electron stable hota hai, bilkul planet ki tarah." — Kyun sahi lagta hai, kyun galat hai

Kyun sahi lagta hai: planets ek inverse-square force ke under Sun ke around stably orbit karte hain; Coulomb force bhi inverse-square hai, isliye analogy perfect lagti hai. Kyun galat hai: electron charged aur accelerating hai (circular motion = centripetal acceleration). Classical electromagnetism kehta hai ki ek accelerating charge energy radiate karta hai (electromagnetic waves). Planets gravitational waves koi appreciable rate par radiate nahi karte; electrons strongly radiate karte hain. Fix / consequence: energy khote khote, electron inward spiral karta aur nucleus mein crash kar jaata. Classical Larmor radiation formula use karke ek proper estimate $\sim 1 0^{- 11}$ – $1 0^{- 10}$ s (roughly ek sau-arabwein second) ke order par collapse time deta hai. Toh classical nuclear atom almost instantly collapse ho jaana chahiye — phir bhi atoms stable hain. Yeh "spiral death" fatal flaw hai.

6. Active recall

Recall Answers cover karo aur khud se quiz karo

Zyaadatar α-particles seedhe through kyun gaye? → atom mostly empty space hai.
Kuch wapas kyun bounce hue? → ek tiny, dense, positive nucleus par head-on hit.
Closest approach find karne wala formula kaunsa hai aur kis principle se? → $r_{0} = \frac{1}{4 π ε _{0}} \frac{4 Z e ^{2}}{m v ^{2}}$ energy conservation se (KE = Coulomb PE).
Rutherford's model ki do failures? → predicts electron spiral/collapse (~ $1 0^{- 11}$ – $1 0^{- 10}$ s mein); continuous (na ki line) spectra predict karta hai.
Electron ke liye centripetal force kya provide karta hai? → electrostatic (Coulomb) attraction.

Recall Feynman: ek 12-saal ke bachche ko explain karo (hidden)

Socho tum hazaaron marbles ek aisi wall par phenk rahe ho jo zyaadatar cling-film se bani hai aur jisme kuch tiny, super-heavy steel balls chupi hain. Tumhare lagbhag saare marbles film se seedhe nikal jaate hain — wall basically empty hai. Lekin kabhi kabhi ek marble kisi steel ball par dead-on lagta hai aur wapas tumhare paas uda ke aata hai. Yeh "wapas aana" hi woh shock hai jo batata hai: us saari empty space ke andar chhote, bhaari, hard lumps chuppe hain. Ek atom mein woh lumps nucleus hain, aur baaki sab empty space hai jisme halke electrons ghoom rahe hain.

Connections

Thomson's Plum Pudding Model — woh model jo is experiment ne overturn kiya
Coulomb's Law — scattering ke peeche inverse-square force
Bohr Model of the Atom — collapse & line-spectrum failures fix karta hai
Atomic Spectra (Line Spectra) — jo Rutherford's model explain nahi kar saka
Discovery of the Proton and Neutron — nucleus ke baad ke constituents
Centripetal Force and Circular Motion — orbiting electron ki physics

Gold-foil scattering experiment kis ne direct kiya (aur kisne perform kiya)?

Ernest Rutherford ne direct kiya; Hans Geiger aur Ernest Marsden ne perform kiya (1909–1911).

Projectiles ke roop mein use kiye gaye α-particles kya the?

Helium nuclei (He²⁺), charge +2e, mass ~4 u.

Gold foil ko extremely thin kyun banaya gaya?

Taaki har α-particle essentially ek hi interaction se guzre, jo clean single-scattering data deta hai.

Observation 1 aur uska conclusion?

Zyaadatar particles seedhe through gaye → atom mostly empty space hai.

Observation 3 aur uska conclusion?

Bahut kam (~1 in 20,000) >90° par wapas bounce hue → tiny, dense, positively charged nucleus.

Distance of closest approach find karne ke liye kaunsa principle use hota hai?

Conservation of energy: initial KE = stopping point par Coulomb PE.

Distance of closest approach r₀ ka formula?

r₀ = (1/4πε₀)(4Ze²)/(mv²).

Nucleus atom se roughly kitna chhota hai?

Radius ~10⁴ guna chhota (~10⁻¹⁴ m vs ~10⁻¹⁰ m).

Rutherford ki orbiting-electron picture mein centripetal force kya provide karta hai?

Nucleus aur electron ke beech electrostatic (Coulomb) attraction.

Rutherford's model ki pehli failure?

Ek accelerating (circling) electron energy radiate karta hai (classical Larmor formula), isliye woh nucleus mein spiral kar jaata hai → predicted collapse ~10⁻¹¹–10⁻¹⁰ s mein.

Rutherford's model ki doosri failure?

Yeh ek continuous spectrum predict karta hai, lekin atoms discrete line spectra dikhate hain.

Rutherford ne actually kya discover kiya?

Atomic nucleus (electron ya neutron nahi).