C. Structure and Properties of Matter · Structure and Properties of MatterFrom Dalton to Rutherford: Evidence for the Nuclear Atom
C3.1 A1.8 A1.10About 70 minutes
Learning goals- I can describe the atomic models of Dalton, Thomson and Rutherford and the evidence for each.
- I can explain the observations and inferences of the gold foil experiment.
- I can explain why the planetary model of the atom could not be the final answer.
- I can use scientific notation to compare the sizes and masses of atomic particles.
Words to know
model
A simplified representation that explains observations and makes predictions; it is revised when new evidence does not fit.
cathode ray
A beam of electrons travelling from the negative electrode (cathode) in an evacuated tube.
alpha particle
A positively charged particle (a helium-4 nucleus: 2 protons and 2 neutrons) given off by some radioactive atoms.
nucleus
The tiny, dense, positively charged centre of an atom, containing protons and neutrons.
line spectrum
Light containing only certain specific wavelengths, seen as separate bright lines.
How do you study something you cannot see?
Nobody has ever looked at an atom the way you look at a maple leaf. Everything we know about the inside of an atom comes from indirect evidence: firing things at atoms, heating them, shining light on them, and then asking which model best explains the results.
In this unit you will follow that story from simple balls to the quantum mechanical model that chemists use today, and then use it to explain the periodic table, the shapes of molecules and the properties of every kind of solid.
Remember from earlier grades: in Grade 9 you drew Bohr-Rutherford diagrams, and in Grade 11 Chemistry (SCH3U, Matter, Chemical Trends, and Chemical Bonding) you used protons, neutrons and electrons, atomic and mass numbers, isotopes, and the electron arrangements of the first 20 elements. This lesson asks why scientists believe atoms are built that way.
What is a model?
A scientific model is a simplified picture that explains observations and makes predictions. A model is never "proven true"; it is kept while it explains the evidence and replaced when it fails. That is not a weakness of science. It is how science works.
Dalton: atoms as solid spheres (1803 to 1808)
John Dalton, an English teacher and chemist, proposed that:
- All matter is made of tiny, indivisible particles called atoms.
- All atoms of one element are identical in mass and properties; atoms of different elements differ.
- Compounds form when atoms combine in fixed, whole-number ratios.
- In a chemical reaction atoms are rearranged, not created or destroyed.
Dalton's theory explained the laws of conservation of mass and definite proportions. Two of his ideas did not last: atoms can be divided (they contain smaller particles), and atoms of one element are not all identical in mass (isotopes, which you met in Grade 11).
Thomson: the electron (1897)
J. J. Thomson studied cathode rays, the glowing beams inside sealed glass tubes with most of the air pumped out. He found that the rays bent towards a positive plate and in a magnetic field, so they were made of negatively charged particles. By measuring how much they bent, he found their charge-to-mass ratio, and it was the same whatever metal the electrodes were made of. These particles were far lighter than any atom. They were later called electrons.
Since atoms are neutral, Thomson pictured the atom as a sphere of positive charge with electrons scattered through it, often called the "plum pudding" model (Canadians might picture blueberries in a muffin). In 1909 Robert Millikan's oil-drop experiment measured the charge on one electron: about 1.60 × 10⁻¹⁹ C. Combined with Thomson's ratio, this gave the electron's mass: about 9.11 × 10⁻³¹ kg, roughly 1/1836 of the mass of a hydrogen atom.
A timeline of atomic models (not to scale). Each model kept what still worked and changed what new experiments could not explain.Rutherford: the nuclear atom (1911)
Ernest Rutherford had already won the 1908 Nobel Prize in Chemistry for his work on radioactivity, much of it done at McGill University in Montréal. Later, in Manchester, his assistants Hans Geiger and Ernest Marsden fired alpha (α) particles (small, fast, positively charged particles from a radioactive source) at gold foil only a few hundred atoms thick, and watched for flashes on a glowing screen.
Observations:
- Most alpha particles went straight through the foil.
- A few were deflected through small angles.
- A very small fraction bounced back towards the source.
Rutherford said it was "almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you." With Thomson's spread-out positive charge, every alpha particle should have gone almost straight through.
Inferences:
- Most of the atom is empty space (most particles passed through).
- The positive charge and almost all of the mass are concentrated in a tiny, dense nucleus (only a direct hit on something small, heavy and positive can push an alpha particle back).
- Electrons move in the space around the nucleus.
The nucleus is about 10⁻¹⁵ to 10⁻¹⁴ m across, while the atom is about 10⁻¹⁰ m across. Rutherford later identified the proton (1919), and James Chadwick discovered the neutron in 1932, which explained why atoms are heavier than their protons alone.
Geiger and Marsden's gold foil experiment, interpreted by Rutherford in 1911 (simplified, not to scale). The rare particles that bounced back showed that the atom's positive charge and mass are packed into a tiny nucleus.Two models compared (not to scale: a real nucleus is about 100 000 times smaller across than its atom). Only a concentrated positive nucleus can push an alpha particle straight back.The problem with Rutherford's model
Rutherford pictured electrons orbiting the nucleus like planets around the Sun. Physicists immediately saw two problems:
- Collapse. According to classical physics, a charged particle moving in a circle is accelerating and should give off electromagnetic radiation, lose energy and spiral into the nucleus in a tiny fraction of a second. Real atoms are stable.
- Spectra. A spiralling electron would give off a smooth rainbow of all colours. But heated hydrogen gives off only a few specific colours of light (a line spectrum).
These failures led Niels Bohr to a new model in 1913, which is the subject of the next lesson. Notice the pattern: the model changed because evidence demanded it.
Worked exampleExample 1: How empty is an atom?
A gold atom has a diameter of about 2.9 × 10⁻¹⁰ m and its nucleus has a diameter of about 1.4 × 10⁻¹⁴ m. (a) How many times wider is the atom than the nucleus? (b) If the nucleus were a 1.0 cm marble, how wide would the atom be?
- (a) Divide: (2.9 × 10⁻¹⁰ m) ÷ (1.4 × 10⁻¹⁴ m) = 2.07 × 10⁴. The atom is about 21 000 times wider.
- (b) Scale up: 1.0 cm × 2.07 × 10⁴ = 2.07 × 10⁴ cm = 207 m.
- So the marble-sized nucleus would sit in an atom about two football fields across, with nothing but a few electrons in all that space.
(a) about 2.1 × 10⁴ times; (b) about 210 m across.
Worked exampleExample 2: Reasoning from evidence
Suppose the gold foil experiment had shown that every alpha particle passed straight through with no deflection at all. Which model would that evidence support, and why?
- Thomson's model spreads positive charge thinly through the whole atom, so the forces on an alpha particle are weak and mostly cancel.
- Weak, cancelling forces mean almost no deflection.
- Rutherford's model has a concentrated nucleus that would deflect at least a few particles strongly, which this imaginary result does not show.
It would support Thomson's plum pudding model, because only a spread-out positive charge lets every particle through undeflected. The real result (rare large deflections) ruled it out.
Worked exampleExample 3: Comparing masses
The mass of a proton is 1.673 × 10⁻²⁷ kg and the mass of an electron is 9.109 × 10⁻³¹ kg. How many electrons have the same mass as one proton? What does this tell you about where an atom's mass is?
- Divide: (1.673 × 10⁻²⁷) ÷ (9.109 × 10⁻³¹) = 1.837 × 10³.
- A proton is about 1837 times as massive as an electron, and a neutron is slightly heavier still.
- So the electrons add almost nothing to the mass; nearly all of it is in the nucleus.
About 1840 electrons (1.837 × 10³). Nearly all of an atom's mass is in the nucleus, as Rutherford inferred.
Just for funRutherford's nucleus is so small that if all the empty space were squeezed out of the atoms in every person on Earth, everyone together would fit in a volume about the size of a sugar cube. (Not recommended as a way to save space on the bus.)
Hands-on activityRutherford's mystery shape
You are going to discover the shape of something you cannot see, just as Rutherford did.
You need: a helper, a flat piece of cardboard or a large baking sheet, a few books, a small box lid or an object with a simple shape (a triangle cut from cardboard, a small plate, a book), 10 marbles or small balls, paper and a pencil. Grown-up note: marbles are a choking hazard; keep them away from young children.
- Your helper hides an object under the cardboard, then props the cardboard up on books so there is a gap all around. You must not peek.
- Roll marbles under the cardboard from different sides. Watch where each one comes out and in what direction.
- On your paper, draw the path of every marble: straight lines for those that went straight through, bent lines for those that bounced.
- After 30 to 40 rolls, sketch the shape you think is hidden. Then look.
What to look for: marbles that come straight back tell you there is a flat face square to their path; marbles that pass straight through mark empty space. You should be able to locate the object and guess roughly how big it is. Rutherford did the same with alpha particles, except his "object" was about 10⁻¹⁴ m across. Discuss: how would a smaller object (a coin) change how often marbles bounce back?
Your turn
1State two parts of Dalton's atomic theory that are still accepted and two that were later changed.
Still accepted: matter is made of atoms; compounds form from atoms in fixed whole-number ratios; atoms are rearranged (not created or destroyed) in reactions. Changed: atoms are not indivisible (they contain electrons, protons and neutrons) and atoms of one element are not all identical in mass (isotopes).
2What evidence showed Thomson that cathode rays were made of negative particles?
The rays were deflected towards a positive plate (and bent in a magnetic field), which only charged particles do; the direction showed the charge was negative.
3Why did Thomson conclude that electrons are found in all atoms?
The charge-to-mass ratio of the particles was the same no matter which metal the electrodes were made of, so the particles were a common part of different kinds of atoms.
4List the three observations of the gold foil experiment and the inference drawn from each.
Most passed straight through → the atom is mostly empty space. A few were deflected slightly → there is a concentrated positive charge that repels them. A very few bounced back → the positive charge and mass are packed in a tiny, dense nucleus.
5Why couldn't Thomson's model explain particles that bounced back?
In Thomson's model the positive charge is spread thinly over the whole atom, so no part of it is concentrated enough to stop and reverse a fast, heavy alpha particle.
6Give two problems with the planetary model of the atom.
Classical physics predicts an orbiting electron should radiate energy and spiral into the nucleus, but atoms are stable; and it predicts a continuous spectrum, but heated elements give line spectra.
7What did Chadwick discover in 1932, and what problem did it solve?
The neutron. It explained why atoms have more mass than their protons alone would give (for example, helium has 2 protons but about 4 times the mass of hydrogen).
More practice: warm-up
1Who discovered the electron?
2What is the charge on an alpha particle?
Positive (2+; it is a helium nucleus).
3What name is given to Thomson's model?
4Who measured the charge on an electron?
Robert Millikan (oil-drop experiment, 1909).
5Where is most of the mass of an atom?
More practice: on your own
1An atom is about 1 × 10⁻¹⁰ m across and its nucleus about 1 × 10⁻¹⁵ m across. If the nucleus were a 2 mm grain of sand, how wide would the atom be?
Ratio = 10⁻¹⁰ ÷ 10⁻¹⁵ = 10⁵. 2 mm × 10⁵ = 2 × 10⁵ mm = 200 m.
2Why did Rutherford use a very thin foil rather than a thick block of gold?
In a thick block, each alpha particle would pass many atoms and be deflected many times (or stopped), so the results could not be traced to single encounters with nuclei. A thin foil gives clear, simple evidence.
3A student says, "Rutherford proved that Thomson was wrong about everything." Correct this statement.
Rutherford kept Thomson's electron and the idea that atoms are neutral with positive and negative parts. He changed where the positive charge is (concentrated in a nucleus, not spread out). Models are revised, not thrown away.
4Millikan found the charge on every oil drop was a whole-number multiple of 1.60 × 10⁻¹⁹ C. A drop has a charge of −8.00 × 10⁻¹⁹ C. How many extra electrons does it carry?
(8.00 × 10⁻¹⁹) ÷ (1.60 × 10⁻¹⁹) = 5 electrons.
5Predict what would happen in the gold foil experiment if the foil were made of aluminium (smaller nuclei, 13 protons instead of 79).
Most particles would still pass straight through, but fewer would be deflected at large angles and the deflections would be smaller, because each nucleus has less positive charge to repel the alpha particles.
Challenge
1A gold-197 nucleus has a radius of about 7.0 × 10⁻¹⁵ m and a mass of about 3.27 × 10⁻²⁵ kg. Estimate its density and compare it with water (1.0 × 10³ kg/m³).
V = (4/3)πr³ = (4/3)(3.1416)(7.0 × 10⁻¹⁵)³ = (4.189)(3.43 × 10⁻⁴³) = 1.437 × 10⁻⁴² m³. Density = 3.27 × 10⁻²⁵ ÷ 1.437 × 10⁻⁴² = 2.3 × 10¹⁷ kg/m³, about 2 × 10¹⁴ times the density of water.
2Explain why the result of the gold foil experiment is good evidence that the nucleus is positive and not negative.
Alpha particles are positive. They were pushed away (deflected outwards and bounced back), which is repulsion. Like charges repel, so the nucleus must be positive. A negative nucleus would attract them and bend their paths inward instead.
3Thomson measured charge-to-mass ratio, and Millikan measured charge. Show how the two together give the electron's mass, using e/m = 1.76 × 10¹¹ C/kg and e = 1.60 × 10⁻¹⁹ C.
m = e ÷ (e/m) = (1.60 × 10⁻¹⁹ C) ÷ (1.76 × 10¹¹ C/kg) = 9.09 × 10⁻³¹ kg, which matches the accepted value of 9.11 × 10⁻³¹ kg to within rounding.
Check your understandingQuiz
1. Which observation from the gold foil experiment led directly to the idea of a tiny, dense nucleus?
2. What did Thomson's cathode-ray experiments show?
3. Which part of Dalton's theory was contradicted by the discovery of isotopes?
4. Why did physicists expect Rutherford's orbiting electrons to spiral into the nucleus?
5. Who discovered the neutron?
6. An atom is about 100 000 times wider than its nucleus. Which statement follows?
For parents and teachersBig idea (C3.1): atomic models changed because experiments produced results the old model could not explain. Your teen should be able to link each model to its evidence (Thomson: cathode rays; Rutherford: gold foil) and explain each inference, not just list names and dates.
How to help: ask "How do they know?" whenever your teen states a fact about atoms. The activity works well with two people; let your teen predict the hidden shape before lifting the cover.
Common difficulties:
- Mixing up observations (what was seen) with inferences (what was concluded). Have your teen sort them into two columns.
- Thinking the plum pudding model was "stupid". It fitted the evidence available in 1904, which is the point of a model.
- Scientific notation errors when dividing powers of ten: 10⁻¹⁰ ÷ 10⁻¹⁵ = 10⁵ (subtract exponents).