Thomson's plum-pudding model — Hinglish notes

1.2.3 · Chemistry › Atomic Structure (Classical)

WHAT is the model?

Thomson ne isko propose kyun kiya?

Electrons abhi abhi mile the → matter mein negatives hain.
Atoms experimentally neutral hain → ek equal positive charge zaroor hoga.
Abhi tak kuch bhi suggest nahi karta tha ki positive charge concentrated hai, isliye sabse simple guess yeh tha ki yeh poore atom mein evenly spread hai.

Yeh stable kyun rehta hai? Uniform positive sphere electrons ko centre ki taraf kheenchta hai; electrons ek dusre ko repel karte hain aur spread ho jaate hain. Ek special arrangement par yeh forces balance ho jaate hain, jo ek stable equilibrium deta hai — yahi woh key feature hai jise hum actually derive kar sakte hain.

DERIVATION — restoring force aur ek electron ki oscillation

Maano ek single electron ek uniform positive sphere ke andar baitha hai jiska total charge $+ e$ aur radius $R$ hai.

Step 1 — Radius $r$ par enclosed charge. Yeh step kyun? Positive charge uniformly spread hai, isliye charge volume ke proportional hai. $q_{in} = e \cdot \frac{\frac{4}{3} π r ^{3}}{\frac{4}{3} π R ^{3}} = e \frac{r ^{3}}{R ^{3}}$

Step 2 — $r$ par us enclosed charge se field (Gauss). Kyun? Ek uniform sphere, radius $r$ par, aise behave karta hai jaise $q_{in}$ centre par rakha ho. $E (r) = \frac{1}{4 π ε _{0}} \frac{q _{in}}{r ^{2}} = \frac{1}{4 π ε _{0}} \frac{e r}{R ^{3}}$

Step 3 — Electron par force (charge $- e$ ). Kyun? $F = q E$ , aur sign isko centre ki taraf point karta hai. $F = - e E = - \frac{e ^{2}}{4 π ε _{0} R ^{3}} r$

Step 4 — Yeh kyun matter karta tha. Kyun? Ek oscillating charge frequency $ν$ ki light radiate karta hai. Thomson ko umeed thi ki yeh $ν$ atomic spectral lines se match karega. $R \approx 1 0^{- 10} m$ daalne par $ν \sim 1 0^{15} Hz$ milta hai — visible light ke liye bilkul sahi order! Yahi early success thi jis wajah se model convincing lagta tha.

Worked examples

Common mistakes

Model kyun abandon kiya gaya

Flashcards

Plum-pudding model kisne propose kiya aur kis saal?

J.J. Thomson, 1904.

"Pudding/dough" ka role kya play karta hai?

Ek sphere of uniform positive charge jo poore atom mein fill hoti hai.

"Plums/raisins" ka role kya play karta hai?

Electrons, positive sphere ke andar embedded hote hain.

Equal positive charge kyun hona chahiye?

Kyunki atoms experimentally electrically neutral hain.

Ek uniform sphere ke andar, electric field

r

ke saath kaise vary karta hai?

E \propto r

(linearly grow karta hai),

1/ r^{2}

nahi.

Charge

+ e

, radius

R

mein ek electron ke liye restoring force constant

k

kya hai?

k = \frac{e ^{2}}{4 π ε _{0} R ^{3}}

Pudding ke andar electron kaunsi motion execute karta hai?

Simple harmonic motion,

ω = e^{2} / (4 π ε_{0} m_{e} R^{3})

Konse experiment ne model ko disprove kiya, aur kaise?

Geiger–Marsden gold-foil: large-angle

α

-scattering ne ek dense nucleus demand kiya.

Kya plum-pudding atom mein nucleus hota hai?

Nahi — positive charge diffuse hai, koi central lump nahi.

Model ke alternative names kya hain?

Watermelon model, raisin-bread model.

Recall Feynman: ek 12-saal ke bachche ko samjhao

Ek soft round jelly ball imagine karo jo thodi "positive" hai. Ab usme har jagah tiny "negative" raisins daal do. Jelly ki positiveness aur raisins ki negativeness cancel ho jaati hai, isliye bahar se ball ka koi charge nahi lagta — yahi ek atom hai! Agar raisin ko nudge karo, jelly use wapas kheench leti hai, toh yeh apni jagah wiggle karta hai. Baad mein, scientists ne in jelly atoms par tiny bullets fire kiye; kuch bullets seedhe wapas bounce ho gayi. Soft jelly yeh nahi kar sakti — isliye beech mein ek hard chota "seed" hona chahiye. Isse jelly idea khatam ho gaya aur humein nucleus mila.

Connections

Discovery of the electron (Thomson's cathode ray tube) — woh finding jo is model ko force karti hai.
Rutherford's nuclear model — woh successor jo ise replace karta hai.
Geiger–Marsden gold foil experiment — disproof.
Gauss's law — woh tool jo $E \propto r$ ek uniform sphere ke andar nikalne ke liye use hota hai.
Simple Harmonic Motion — embedded electron ka $F = - k r$ mathematics.
Bohr model — orbits aur spectra ke liye baad ka fix.