1. Atoms and the Periodic Table

If every oxygen atom has the same mass, the mass of oxygen in a compound is the number of oxygen atoms times that mass. With a fixed mass of nitrogen (so a fixed number of nitrogen atoms), the oxygen masses in N₂O, NO and NO₂ are in the ratio of oxygen atoms per nitrogen atom: ½ : 1 : 2, or 1 : 2 : 4.

No. He had masses and not formulas, and he guessed that the commonest compound of two elements had one atom of each (water as HO). That is why his table of atomic weights was wrong for several elements. Gay-Lussac's volumes and Avogadro's idea, in 1811, were needed to put it right (Unit 10).

Atoms are not indivisible, as the next three experiments show, and atoms of one element are not all alike, as the fifth shows (isotopes). What survives is the central idea: reactions rearrange atoms that keep their identity.

In 1897 nobody had heard of photons: Einstein proposed them in 1905. Many physicists thought cathode rays were waves, something like light. Others thought they were streams of charged particles.

Light has no charge, so electric plates and magnets cannot bend it. These rays bend, and always toward the positive plate, so they carry negative charge. That bend is the evidence that they are particles and not light. (Hertz had looked for the bend earlier and not seen it, because gas left in his tube hid the effect. Thomson pumped his tube out better and saw it.)

A large voltage (2,000 V here) is held between the cathode, which is negative, and the anode, which is positive. The strong field pulls electrons out of the cathode's surface (in Thomson's tube, positive ions from the little gas left in it also knocked electrons loose), and the anode attracts them. They fly through a slit in the anode as a thin beam. The tube is pumped almost empty so they do not hit air on the way.

Each electron gains energy eV, so ½mv² = eV, which gives its speed. (Modern tubes heat the cathode so electrons boil off it.)

Both fields push the beam sideways, but differently. The electric push, eE, is the same at any speed. The magnetic push, evB, grows with speed. Make them cancel, eE = evB, and the speed drops out: v = E / B.

Thomson needed the speed to turn the bend into e/m, and the magnet is how he measured it. A magnetic force never speeds the electrons up or slows them down. It only turns them.

The magnetic force on a moving charge is F = q v × B, a vector product, so it points at right angles to both the motion and the field. Reverse B and the product reverses, so the push flips. Reverse the sign of the charge instead and it flips too.

That gives a second way to find the sign of a charge: in the same fields, negative particles bend opposite to positive ones.

Yes: e = 1.602 × 10⁻¹⁹ coulombs (Millikan's own result was about 1.59 × 10⁻¹⁹). It is a very small number because a coulomb is a very large amount of charge: about 6 × 10¹⁸ electrons.

Oil does not evaporate in the chamber, so a drop keeps the same weight. (Water drops shrink as they dry.) A fine spray from an atomizer picks up charge by friction, and Millikan could change a drop's charge with X-rays that knocked electrons on or off, then watch its balance voltage jump to a new value.

From its radius. With the field off, a drop falls at a steady speed set by air drag (Stokes' law), and that speed gives the radius, so the mass is (4/3)πr³ times the density. Here the radius is shown for you.

A heavier drop needs a bigger voltage to hang still, yet the charge you calculate lands on the same ladder every time. If charge could take any value you would get any number at all. You get steps.

Because for a single atom it is a matter of chance, not of its history: an atom that has survived for a billion years is no more likely to decay in the next second than a new one. Only the crowd is regular. Quantum theory (Unit 2) says the chance is built into nature.

Living things take in carbon, including a tiny steady share of radioactive carbon-14 made by cosmic rays in the air. When they die the intake stops and the carbon-14 decays with its half-life of 5700 years. The fraction left in a bone, or in a piece of wood, gives the time since death, back to about 50,000 years (nine half-lives).

Because activity goes with the rate of decay, and an isotope with a short half-life has more atoms decaying each second per gram. Uranium-238 has a half-life of billions of years, radium-226 of 1600. That is why the Curies needed tonnes of ore to get a gram of radium.

Alpha particles are helium nuclei: two protons and two neutrons, charge +2. Radioactive atoms such as radium shoot them out at about 5% of the speed of light. They are about 7,300 times heavier than an electron, so electrons barely deflect them, like a bowling ball through ping-pong balls.

Gold can be hammered into a foil only a few thousand atoms thick, so most alphas meet at most one nucleus. And a gold nucleus has charge +79, so it pushes hard.

A screen coated with zinc sulfide flashes where an alpha hits it. Geiger and Marsden counted the flashes through a microscope in a dark room, for hours at a time.

Not yet. This experiment shows positive charge gathered in a tiny core. Rutherford identified the proton, the particle that carries one unit of that charge, a few years later, and Chadwick found the neutron in 1932.

Fire fast electrons at it. Now and then one knocks an electron out of an atom's innermost shell. An electron from a higher shell falls into the hole, and the atom gives off the energy difference as an X-ray. That energy depends on how strongly the nucleus pulls on the inner electrons, which depends on its charge Z.

The electron that falls in is pulled by the nucleus, but one electron left in the inner shell screens one unit of the charge, so the pull is that of Z − 1.

Mass depends on neutrons as well as protons. Nickel has one more proton than cobalt, but its common isotopes carry fewer neutrons, so its average mass comes out slightly lower. Chemistry follows the protons.

Atoms are turned into ions by knocking off an electron with an electron beam, then speeded up by an electric field so they all gain the same energy, then bent by a magnet. The radius is r = (1/B)√(2mV/q), so lighter ions bend more tightly and each isotope lands in a different place. The strength of each signal says how common that isotope is.

Chemistry works with huge numbers of atoms at once, so the average is what counts: the weighted average over all the isotopes. It is the number you use to count atoms from a mass.

Very nearly. The isotope mix is almost the same in samples from all over Earth, which is why one number works. (Small variations exist, and are used to trace where things came from.)