Rutherford's Model of Atom

Setting up the experiment. Rutherford's team aimed a narrow beam of fast-moving alpha ($\alpha$) particles — helium nuclei, each carrying a positive charge — at a sheet of gold foil only about $1000$ atoms thick. Gold was chosen because it can be beaten into an extremely thin sheet without tearing. A circular screen coated with zinc sulfide, which glows with a tiny flash wherever a particle strikes it, surrounded the foil so that the scattered particles could be tracked in every direction, not just straight ahead.

Three observations, three conclusions. Each observation Rutherford recorded points to exactly one feature of the atom's structure, and the three together assemble the whole model.

• Most alpha particles sailed straight through the foil as if nothing were there at all. This can only happen if most of the volume inside an atom is empty space, with nothing dense enough in the way to disturb a fast, heavy particle.
• A small fraction of the particles were deflected through noticeable angles. A moving positive charge only gets pushed off course by another concentration of charge of the same sign repelling it, so there must be a region of concentrated positive charge somewhere inside the atom.
• A very small number — about $1$ in every $12{,}000$ — bounced back almost the way they had come, deflected by close to $180°$. Only a very compact, very massive obstacle could reverse a fast alpha particle so completely; a spread-out or lightweight object would merely nudge it aside. So this positive charge, and almost the entire mass of the atom, must be packed into a region of very small volume.

The nuclear model. Putting the three conclusions together, Rutherford proposed that every atom has a tiny, dense, positively charged centre called the nucleus, carrying almost the whole mass of the atom, with electrons revolving around the nucleus in circular orbits — much as planets orbit the Sun — while the rest of the atom, by far the greater part of its volume, is empty space.

Rutherford's reasoning is really an exercise in ruling out explanations that do not fit the evidence, one observation at a time. Thomson's "plum pudding" model spreads the positive charge evenly across the whole atom, like soft dough — there is no place in it dense or charged enough to turn back a fast alpha particle, so if that model were correct, every alpha particle should pass through with at most a gentle wobble. That is exactly what most particles did, which is why the straight-through majority does not, by itself, disprove Thomson's model. The particles that decide the matter are the rare, large-angle ones. A deflection of nearly $180°$ means the alpha particle met something that could stop it and hurl it almost straight back — the kind of encounter you get when a fast, light object meets something both far more massive and far more concentrated, not a slow, soft push from spread-out charge. Because such head-on encounters were so rare (about $1$ in $12{,}000$), whatever is doing the deflecting must occupy only a tiny fraction of the atom's cross-section: an alpha particle has to be aimed almost exactly at this object to be turned back, and most particles simply never come close enough to feel it. This single rare event, then, forces two conclusions at once — the deflecting object is small in size (so a direct hit is rare) yet large in mass and charge (so a direct hit reverses the particle completely) — and that combination is precisely the nucleus. The gentle deflections of the "small fraction" group are the in-between cases: alpha particles that pass near, but not straight at, the nucleus, and feel only a partial repulsion.

Question: In one run of the experiment, $60{,}000$ alpha particles are fired at the gold foil. Using Rutherford's finding that about $1$ in $12{,}000$ particles bounces back by close to $180°$, estimate (a) how many particles are expected to bounce back, and (b) what this tells us about the size of the nucleus compared to the whole atom.

Step 1. Set up the proportion. If $1$ particle out of every $12{,}000$ bounces back, then out of $60{,}000$ particles the expected number that bounce back is $\dfrac{60{,}000}{12{,}000} \times 1 = 5$.

Step 2. Interpret the count. Five particles is a tiny fraction — just $5$ out of $60{,}000$, or about $0.008\%$ — of the whole beam. Every one of the other $59{,}995$ particles either passed straight through or was only slightly deflected, meaning it never came close enough to a nucleus to be strongly repelled.

Step 3. Connect the fraction to the geometry of the atom. For a large-angle bounce-back to be this rare, an alpha particle must be aimed almost exactly at a nucleus for it to happen — and since only a tiny share of all the particles fired manage that, the nucleus can only be occupying a correspondingly tiny share of the atom's total cross-section. This is exactly the size argument Rutherford used: a rare direct hit means a small target.

Answer: about 5 of the 60,000 particles are expected to bounce back, and this tiny fraction confirms that the nucleus occupies only a very small volume of the atom, even though it holds almost all of the atom's mass and positive charge.

• Saying alpha particles are neutral — they are positively charged, and it is exactly this shared charge that makes the repulsion (and hence the deflection) happen.
• Thinking a large fraction of alpha particles were deflected — only a small fraction were deflected at all, and a very small fraction ($1$ in $12{,}000$) bounced straight back; the overwhelming majority passed straight through undisturbed.
• Confusing "small in size" with "small in mass" — the nucleus is small in volume but contains almost the entire mass of the atom; both facts come from the same rare bounce-back observation, not from two separate ones.
• Mixing up Thomson's and Rutherford's models — Thomson spread the positive charge through the whole atom with no dense centre; Rutherford's model concentrates it into a tiny nucleus, leaving the rest of the atom empty.

Ask the tutor: if you want to see how each of Rutherford's three observations maps to its exact conclusion, or want a worked proportion problem with different numbers, ask the AI tutor to walk through it step by step.