Noesis
1.2.3Atomic Structure (Classical)

Thomson's plum-pudding model

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🇮🇳 Yeh note Hinglish mein padho →

WHAT is the model?

WHY did Thomson propose it?

  1. Electrons had just been found → matter contains negatives.
  2. Atoms are experimentally neutral → an equal positive charge must exist.
  3. Nothing yet suggested the positive charge was concentrated, so the simplest guess was that it is spread evenly over the whole atom.

HOW does it stay stable? The uniform positive sphere pulls electrons toward the centre; electrons repel each other and spread out. At a special arrangement these forces balance, giving a stable equilibrium — this is the key feature we can actually derive.

DERIVATION — restoring force & oscillation of one electron

Let a single electron sit inside a uniform positive sphere of total charge +e+e, radius RR.

Step 1 — Charge enclosed at radius rr. Why this step? The positive charge is spread uniformly, so charge is proportional to volume. qin=e⋅43πr343πR3=e r3R3q_{\text{in}} = e\cdot\frac{\tfrac{4}{3}\pi r^3}{\tfrac{4}{3}\pi R^3} = e\,\frac{r^3}{R^3}

Step 2 — Field at rr from that enclosed charge (Gauss). Why? A uniform sphere acts, at radius rr, as if qinq_{\text{in}} sat at the centre. E(r)=14πε0qinr2=14πε0e rR3E(r)=\frac{1}{4\pi\varepsilon_0}\frac{q_{\text{in}}}{r^2}=\frac{1}{4\pi\varepsilon_0}\frac{e\,r}{R^3}

Step 3 — Force on the electron (charge −e-e). Why? F=qEF=qE, and the sign makes it point back to centre. F=−eE=−e24πε0R3 rF=-eE=-\frac{e^2}{4\pi\varepsilon_0 R^3}\,r

Step 4 — WHY this mattered. Why? An oscillating charge radiates light of frequency ν\nu. Thomson hoped this ν\nu would match atomic spectral lines. Plugging R≈10−10 mR\approx10^{-10}\,\text{m} gives ν∼1015 Hz\nu\sim10^{15}\,\text{Hz} — right order for visible light! This early success is why the model felt convincing.

Figure — Thomson's plum-pudding model

Worked examples

Common mistakes

Why the model was abandoned

Flashcards

Who proposed the plum-pudding model and in what year?
J.J. Thomson, 1904.
What plays the "pudding/dough" role?
A sphere of uniform positive charge filling the whole atom.
What plays the "plums/raisins"?
The electrons, embedded inside the positive sphere.
Why must an equal positive charge exist?
Because atoms are experimentally electrically neutral.
Inside a uniform sphere, how does the electric field vary with rr?
E∝rE\propto r (grows linearly), not 1/r21/r^2.
What is the restoring force constant kk for an electron in charge +e+e, radius RR?
k=e24πε0R3k=\dfrac{e^2}{4\pi\varepsilon_0 R^3}.
What kind of motion does an electron execute inside the pudding?
Simple harmonic motion, ω=e2/(4πε0meR3)\omega=\sqrt{e^2/(4\pi\varepsilon_0 m_e R^3)}.
Which experiment disproved the model, and how?
Geiger–Marsden gold-foil: large-angle α\alpha-scattering required a dense nucleus.
Does the plum-pudding atom have a nucleus?
No — positive charge is diffuse, no central lump.
Alternative names for the model?
Watermelon model, raisin-bread model.
Recall Feynman: explain to a 12-year-old

Imagine a soft round jelly ball that is slightly "positive." Now stick tiny "negative" raisins all through the jelly. The jelly's positiveness and the raisins' negativeness cancel out, so from outside the ball seems to have no charge at all — that's an atom! If you nudge a raisin, the jelly pulls it back to where it was, so it wiggles in place. Later, scientists shot tiny bullets at these jelly atoms; some bullets bounced straight back. Soft jelly can't do that — so there must be a hard little "seed" in the middle. That killed the jelly idea and gave us the nucleus.

Connections

  • Discovery of the electron (Thomson's cathode ray tube) — the finding that forced this model.
  • Rutherford's nuclear model — the successor that replaced it.
  • Geiger–Marsden gold foil experiment — the disproof.
  • Gauss's law — the tool used to get E∝rE\propto r inside a uniform sphere.
  • Simple Harmonic Motion — the F=−krF=-kr mathematics of the embedded electron.
  • Bohr model — later fix for orbits and spectra.

Concept Map

matter has negatives

needs equal positive

positive charge

negatives embedded

Gauss's law

field E = e r / 4πε₀R³

Hooke's law form

ω = sqrt k/m

radiates light

balances repulsion

Electron discovered 1897

Puzzle: atoms neutral

Plum-pudding model 1904

Uniform positive sphere R~10⁻¹⁰ m

Electrons stuck inside

Enclosed charge q ∝ r³/R³

Restoring force F = -k r

Simple harmonic motion

Oscillation frequency ν

Predicts ν~10¹⁵ Hz visible

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, 1897 me Thomson ne electron discover kiya — matlab atom ke andar negative charge hota hai. Lekin atom to overall neutral hai, to positive charge kahan hai? Thomson ne socha ki positive charge ek soft ball (pudding/jelly) ki tarah pure atom me faila hua hai, aur electrons us jelly me raisins (kishmish) ki tarah dhanse pade hain. Positive aur negative cancel ho jate hain, isliye atom bahar se neutral dikhta hai. Isko watermelon model bhi kehte hain — seeds hi electrons.

Ab thoda physics ka mazza: agar ek electron ko centre se thoda hilaao, to Gauss's law ke hisaab se sirf andar wala positive charge use kheenchta hai, aur wo charge r3r^3 ke proportional hota hai. Isliye field E∝rE\propto r (linear!), na ki 1/r21/r^2 — yeh point exam me common trap hai. Result: force F=−krF=-kr milta hai, exactly Hooke's law jaisa, to electron SHM karta hai. Is oscillation ki frequency ν∼1015\nu\sim10^{15} Hz nikalti hai jo visible light ke aas-paas hai — isi wajah se model pehle sahi laga.

Par model fail ho gaya. Rutherford ke gold-foil experiment me kuch alpha particles seedha peeche bounce ho gaye. Agar positive charge jelly ki tarah faila hota, to itna bada deflection possible hi nahi. Iska matlab positive charge ek chhote, dense nucleus me concentrated hai. So yaad rakho: plum-pudding me koi nucleus nahi hota, electrons orbit nahi karte — wo bas embedded hote hain. Yeh galtiyan sabse zyada hoti hain, inhe pakka clear rakhna.

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Connections

Rutherford's gold-foil experiment — nuclear modelChemistry · 1.2.4Gauss's law — integral form, choosing Gaussian surfacesPhysics · 1.8.6Simple harmonic motion — definition, restoring force F = −kxPhysics · 1.6.1Bohr model of hydrogen — postulates, radius rₙ = 0.529 n² - Z Å, energy Eₙ = −13.6 Z² - n² eVChemistry · 1.2.7Discovery of electron (Thomson, cathode rays), proton (Goldstein), neutron (Chadwick)Chemistry · 1.2.2Rutherford's gold-foil experiment — nuclear modelChemistry · 1.2.4