A full lesson: a cartoon movie to start, then Thomson's plum pudding and the clue from line spectra, the Geiger–Marsden gold-foil experiment, how small the nucleus really is, why most alpha particles fly straight through, why gold and a thin foil, NEET shortcuts, problems to solve yourself, and 12 MCQs.
Most balls fly straight through the loose straw, but one comes back: something small, hard and heavy is hiding inside. Rutherford found the same thing inside every atom: a tiny, dense, positive nucleus.
After the harvest, Kabir and Meera play a game at the edge of the field. Kabir throws small rubber balls at a big, loose haystack. Almost every ball pushes through the straw and rolls out on the far side, where Meera collects it. Then one ball comes flying straight back at Kabir. They dig into the hay and find an old iron ball, small, hard and heavy, hidden near the middle.
In 1911 Ernest Rutherford's team, Hans Geiger and Ernest Marsden, played the same game with atoms. Their "balls" were alpha particles and their "haystack" was a gold foil. Most particles went straight through, but a few came back. Rutherford said it was as if you fired a heavy shell at a piece of tissue paper and it came back and hit you. That surprise gave us the nucleus.
"One ball coming back tells you more than a hundred going through. It says: somewhere inside, there is something small, heavy and hard to push. In the atom, that something is the nucleus."
"If the iron ball were the size of a football instead of a cricket ball, would more balls come back, or fewer?"
More. The chance of a big deflection depends on how much of the target area the hard object blocks. Because so few alpha particles came back, the nucleus must block a tiny part of the atom: it is very small.
In 1897 J. J. Thomson showed that electrons are the same in the atoms of every element. An atom is neutral, so it must also hold an equal positive charge. In 1898 Thomson proposed that the positive charge is spread uniformly through the whole atom, with the electrons embedded in it like seeds in a watermelon: the plum pudding model. Light gave a second clue about atoms. Switch between the two views.
The positive charge fills the whole atom. Its mass is spread out too, so nothing inside is small and heavy.
A glowing filament or hot dense matter gives every wavelength: the atoms are close and disturb each other.
In a neon sign or a flame, atoms are far apart, so each radiates almost alone. The lines are a fingerprint of the element.
"Line spectra tell us each atom has its own fixed set of energies. Any model of the atom must explain them. Thomson's model could not, and as we will see, it also failed the gold-foil test."
A bismuth source (²¹⁴Bi) gives 5.5 MeV alpha particles. Lead bricks with a slit make a narrow beam that hits a gold foil only 2.1 × 10⁻⁷ m thick. A zinc sulphide screen with a microscope can be rotated around the foil; every alpha particle that hits it makes a tiny flash. Drag the detector (or use the slider) and watch the flash rate at each angle θ.
Lead bricks absorb every alpha particle except those passing through the slit, so the beam is narrow and parallel.
Gold can be beaten into a very thin foil, so each alpha particle usually meets only one nucleus closely.
Each alpha particle gives one flash (scintillation). Counting flashes at each θ gives the number scattered against angle. The whole set-up is in a vacuum.
"Notice how steeply the counts fall as the angle grows. The graph is plotted on a log scale: going from 30° to 150°, the count drops about two hundred times. But it never becomes zero."
Zoom from a sheet of gold atoms down to a single nucleus. Each step of the slider makes the picture ten times larger. Watch how long the screen stays empty between the electron cloud and the nucleus.
With a nucleus of 10⁻¹⁵ m, the ratio becomes 10⁵. So the atom is 10⁴ to 10⁵ times wider than its nucleus.
Volume goes as the cube of the radius. Almost all of this volume is empty space.
A marble at the centre of a cricket ground, with a few specks of dust (electrons) near the boundary rope.
"Ratio questions are where NEET catches students. Radius ratio ten to the four means volume ratio ten to the twelve. Always ask yourself: radius, area or volume?"
Here is a zoomed view of a few atoms in the foil. Fire alpha particles at them using each model. In Thomson's model the positive charge is spread out, so the electric force is never strong. In Rutherford's model all the positive charge sits in a tiny centre, so a close pass feels a huge repulsion.
Most of the atom is empty space. A particle that passes far from every nucleus feels almost no force.
Only particles that pass fairly close to a nucleus are turned noticeably.
Turning back needs a huge force from a small, dense, positive centre. This group is part of the 0.14 %, not separate.
"The alpha particle never touches the nucleus. It is pushed back by electric repulsion before it gets there, like a ball rolling up a steep hill and rolling back. Electrons are far too light to turn a heavy alpha particle."
"What happens to the number of large-angle deflections if we use slower alpha particles?"
More of them. A slower particle can be turned back from farther away, so a bigger part of the atom's area counts as "close". Lesson 2 makes this exact with the distance of closest approach.
Rutherford's analysis made two simplifying assumptions: each alpha particle is scattered by only one nucleus, and the nucleus is so heavy that it stays at rest. Choose a foil metal and a thickness, and see when those assumptions hold.
About 1000 atomic layers in 2.1 × 10⁻⁷ m. Thick foils give many small kicks that add up and spoil the analysis.
The gold nucleus is about 50 times heavier than the alpha particle, so it can be taken as stationary.
Labs fire light ions at thin films in computer chips and count the ones that bounce back to find which atoms are present and how deep.
A few deflected by large angles ⇒ positive charge and almost all mass in a tiny nucleus.
Radius ratio 10⁴ to 10⁵. Volume ratio 10¹² to 10¹⁵.
For N fired: about 0.0014 N beyond 1° and N/8000 beyond 90°.
Beyond NCERT, but useful: N(60°)/N(90°) = sin⁴45°/sin⁴30° = 4.
Source, collimator, target, detector. Vacuum chamber, rotatable microscope.
Line spectrum = fingerprint of the element. Thomson's model could not explain it.
"NEET loves matching each observation with its conclusion. Most go straight: empty space. A few turn a lot: a small, dense, positive nucleus. Learn those two lines and the size ratios, and these marks are yours."
Cover the solution, write the formula, and solve on paper. Open the hint only if you are stuck for more than a minute.
An atom has radius 10⁻¹⁰ m and its nucleus has radius 10⁻¹⁴ m. Find the ratio of their radii and of their volumes.
Volume ∝ r³.
In a model of the atom, the nucleus is a marble of diameter 1 cm. Using a size ratio of 10⁴, how wide is the model atom?
Multiply the nucleus size by the ratio.
One million alpha particles hit the gold foil. Using the NCERT fractions, estimate how many are deflected by more than 1°, and how many by more than 90°.
0.14 % = 0.0014; 1 in 8000 = 1/8000.
Find the speed of a 5.5 MeV alpha particle (m = 6.64 × 10⁻²⁷ kg, 1 MeV = 1.6 × 10⁻¹³ J).
K = ½ m v², so v = √(2K/m).
The gold foil is 2.1 × 10⁻⁷ m thick. Taking a gold atom to be about 2 × 10⁻¹⁰ m across, how many atomic layers does an alpha particle cross? Why do most still pass straight?
Divide the thickness by the size of one atom.
Write the reason first, then click.
Score: 0 / 12
| If the question says… | Write this first | The trap |
|---|---|---|
| "most α particles pass undeflected" | atom is mostly empty space | Saying "the nucleus is large" or "electrons are absent" |
| "a few deflected through large angles" | small, dense, positive nucleus | Crediting the electrons; they are about 7300 times lighter than α |
| "plum pudding / Thomson model" | positive charge spread uniformly | Mixing it up with the nuclear model |
| "ratio of atomic to nuclear size" | radius 10⁴ to 10⁵; volume 10¹² to 10¹⁵ | Giving the radius ratio for a volume question |
| "fraction scattered beyond 90°" | about 1 in 8000 | Treating it as separate from the 0.14 % beyond 1° |
| "why a thin gold foil" | single scattering; gold beaten thin, heavy nucleus | Saying "gold is a good conductor" |
| "line spectrum from" | rarefied (low-pressure) excited gas | Choosing a hot filament or dense gas (continuous) |
| "α turned back at the nucleus" | repelled before contact | Picturing a bounce off a hard surface |
Lesson 2 follows a single alpha particle: its path, the impact parameter, the distance of closest approach, and the energy of an electron orbiting the nucleus. Lesson 3 shows why that classical orbiting electron should collapse, and how Bohr rescued the atom.
Values used: e = 1.6 × 10⁻¹⁹ C, 1 MeV = 1.6 × 10⁻¹³ J, m_α = 6.64 × 10⁻²⁷ kg (4 u), gold Z = 79, A = 197, atom ≈ 10⁻¹⁰ m, nucleus ≈ 10⁻¹⁵ to 10⁻¹⁴ m.
Follow the four steps: understand it, remember it, try it, then prove it with past papers.