OCR GCSE Physics

How the model of the atom changed

Scientists build models of the atom to explain the evidence they have, and change the model when new evidence does not fit. The order matters because each model was a response to an experiment the one before could not explain.

After the electron was discovered, J. J. Thomson proposed that an atom is a ball of positive charge with negatively charged electrons embedded in it, which is often called the plum pudding model. It explained why atoms are neutral overall, since the positive charge and the electrons balance.

Hans Geiger and Ernest Marsden, working with Ernest Rutherford, fired alpha particles (which are positively charged) at a very thin sheet of gold foil and detected where they went. Most passed straight through, a small number were deflected through large angles and a very few bounced almost straight back. The plum pudding model predicted only small deflections, so it could not explain this. Rutherford concluded that the positive charge and nearly all the mass are concentrated in a tiny nucleus at the centre, and that the rest of the atom is mostly empty space with electrons around it. A particle only bounces back if it meets something small, dense and positive, which repels it.

Niels Bohr then changed the model again to say that electrons orbit the nucleus at set distances, in fixed energy levels, rather than anywhere. This explained why atoms emit and absorb radiation only at particular frequencies, and it is the model most often drawn today. Later work showed that the nucleus itself contains positively charged protons and uncharged neutrons, the neutron being identified by James Chadwick.

Each new model came from different scientists testing and building on each other's results, and a model is accepted only when the results of experiments agree with it.

The structure of the atom

An atom has a positively charged nucleus surrounded by negatively charged electrons. The radius of the nucleus is many thousands of times smaller than the radius of the atom, but almost all of the mass of the atom is in the nucleus because electrons have very little mass.

An atom has the same number of electrons as protons, so it has no overall charge. Atoms are typically about $1 \times 10^{-10}\ \mathrm{m}$ across, and small molecules are of the same order of magnitude.

It is easy to mix up the words for particles. An atom is a single particle of an element. A molecule is two or more atoms joined together, as in water or oxygen. Protons, neutrons and electrons are subatomic particles, which are smaller than an atom and are what atoms are made of.

Density

The density of a material is its mass per unit volume. It says how tightly the mass is packed.

$\rho$ (the Greek letter rho) is the density in kilograms per cubic metre (kg/m³), $m$ is the mass in kilograms and $V$ is the volume in cubic metres. Densities are often given in g/cm³, and $1\ \mathrm{g/cm^3} = 1000\ \mathrm{kg/m^3}$. Volumes need converting with care, since $1\ \mathrm{m^3} = 1\,000\,000\ \mathrm{cm^3}$.

Worked example

A steel block measures 5.0 cm by 4.0 cm by 3.0 cm and has a mass of 0.472 kg. Find its density in kg/m³.

The same equation rearranged gives $m = \rho V$. A tank holding 0.25 m³ of water, which has a density of 1000 kg/m³, holds $1000 \times 0.25 = 250$ kg of water.

Density and the states of matter

In a solid the particles are packed closely in a regular pattern and vibrate about fixed positions. In a liquid they are also close together but arranged irregularly and free to move past each other. In a gas they are far apart and move freely at random. Since the same mass of particles takes up much more space as a gas, gases have far lower densities than solids and liquids. Solids are usually a little denser than the same substance as a liquid, because the regular arrangement is usually slightly more compact. Water is a well-known exception, since ice is less dense than liquid water and floats.

Mass does not change when a substance changes state, because the same particles are still there. Only the volume changes, and so the density does. If 1.0 kg of water with a volume of $1.0 \times 10^{-3}\ \mathrm{m^3}$ freezes and the volume increases by about 9%, the density falls from 1000 kg/m³ to about 917 kg/m³.

Practical: measuring density

The apparatus used depends on the object.

For a regular solid, measure the lengths with a ruler or, for a more precise value, a micrometer or vernier callipers, calculate the volume from them, and measure the mass on a balance. Divide the mass by the volume.

For an irregular solid that sinks, measure its mass on a balance. Find its volume by lowering it into a eureka can (a can with a spout, filled to the spout) and collecting the water that overflows in a measuring cylinder. The volume of the water displaced equals the volume of the object, which is the principle Archimedes used. Alternatively, lower it into a measuring cylinder part-filled with water and read the volume before and after. An object that floats can be pushed under with a thin, dense sinker of known volume.

For a liquid, place a measuring cylinder on a balance and set the balance to zero, then pour in a volume of the liquid and read both the volume and the mass. The reading of volume is taken with the eye level with the bottom of the curved surface (the meniscus).

Repeating the measurement and finding a mean reduces the effect of random errors. Air bubbles stuck to an object, water left on it, and reading the scale from an angle all cause errors in the volume.