IB Physics/Atomic and Nuclear Physics
7.1 Atoms and their constituents
The idea of Millikan's oil drop experiment was to have very small oil drops which had some charge balanced between two electric plates. By knowing the strength of the field between the plates, it was possible to calculate the amount of force being applied per charge on the drop, which, if it was floating, would be exactly the same as the force of gravity downwards. From this, it is possible to find the mass to charge ratio of the drops.
The mass of the drop was then measured by cutting the field and measuring it's terminal velocity and using stokes equation. This allowed the charges on the drops to be found, and it was found that the smallest difference between these charges was 1.6 x 10-19 C, the charge of a single electron.
If a mass is being suspended by an electric field, then mg = qE (mass x gravity = charge x electric field strength). Electric field strength can be can be expressed as V/d, (potential difference divided by distance) for calculation purposes.
The results showed that the minimum difference between charges was 1.6 x 10-19 C and so this must be the smallest unit of charge possible.
This means that charge must be quantized (only comes in discrete chunks rather than being continuous), and the quantum of charge was 1.6 x 10-19 C.
An electron gun relies on the principle of thermonic emission. There is a large PD created between two metal plates in a vacuum. The cathode (the negative one from which the electrons come) emits a bunch of electrons. They accelerate towards the anode (the positive plate), which has a hole in it, and so some of the electrons fly through and create a sort of beam of electrons (originally called a cathode ray).
Cathode rays can be deflected by both electric and magnetic fields, and act as negatively charged particles would in such fields. Both these properties can be explained by the fact that they are actually electrons.
Thompson's experiment involved using electric and magnetic fields to exactly cancel each other's effects and allow an electron to pass undeflected. The electric field is then removed and the radius of curvature is measured. The equations then simplify down to give an expression for e/m in which all the other terms are known, and so the ratio of charge to mass could be accurately found.
By knowing the charge of an electron (Millikan) and the charge to mass ratio (Thompson) it is possible to find the mass of an electron. That makes Thompson the discoverer of the electron (hooray for him).
The alpha particle scattering experiment (by Rutherford/Geiger+Marsden) involved firing alpha particles at a sheet of very thin gold foil, and detecting where they went (with a screen).
The results of the above experiment were that the majority of alpha particles passed straight through. Of those which were deflected, many were deflected through very large angles, and even straight back at the source. This result suggested that atoms consisted mostly of empty space, with a small nucleus of high positive charge.
Rutherford's model was that around the small, highly charged nucleus, electrons orbited like planets around the sun. This created many more questions. Why didn't the electrons emit radiation and lose energy? How would they be kept in a constant orbit?
7.2 Nuclei and their constituents
Radioactive decay is basically atoms (or more specifically nuclei) spontaneously breaking off small parts (alpha, beta and gamma particles) of themselves. This was accidentally discovered due to the effects of these particles on photographic film which was being kept in a drawer with them.
This lead to a systematic analysis of such particles, and the elements which produced them. The three different types mentioned above were found and separated, and the effect on the atoms undergoing this process (changing elements from one type to another) was examined.
The three types of radiation were first divided by their ionising power. Rutherford later showed an alpha particle to be the nucleus of a helium atom by measuring their emission spectra. Beta particles were found to be free electrons, but emitted from the nucleus as a result of the changes which occurred in it. Gamma rays were found to be a type of very high frequency electromagnetic radiation.
The products of alpha and beta decay are quite easy to find. Simply write out and balance the nuclear equations.
AZX -> A-4Z-2Y + 42He. The specific isotope represented by Y can then be determined.
Radiation tends to ionise (strip the electrons from) gases when it passes through. This fact is used for the detection of radiation with Geiger counters. (No real detailed knowledge is required here.)
AZX : A is the mass number, the number of nucleons or whatever else you'd like to call it. I find it easiest to think of it as the number of protons + the number of neutrons. Z is the proton number, the atomic number i.e. the number of protons. To find the number of neutrons, obviously, subtract Z from A: A - Z = Number of Neutrons. The number of electrons is most commonly equal to the number of protons. ie, z is equal to number of protons which is equal to number of electrons: Z = P = N.
Artificial transmutation : When atoms decay, they change into different atoms, and this is called artificial transmutation. Atoms usually only lose alpha and beta particles (gamma is just a loss of energy, so not relevant here). An alpha particle is 2 protons and 2 neutrons. A beta particle is 1 negative charge, which turns a neutron into a proton in the nucleus. These facts can be put together to predict the results of nuclear equations. Transmuation also occurs when atoms of one element change into atoms of another element during fusion reactions, or during bombardment of an element with alpha particles or other small nuclear particles. An example is the bombardment of uranium by deturions to create plutonium.
Describe how the reaction between N and He led to the discovery of the proton : By bombarding nitrogen nuclei with alpha particles, Rutherford caused the ejection of hydrogen nuclei and the production of a new oxygen nucleus. As a result, the proton was discovered.
The proton is the thing in the nucleus of a hydrogen atom, and there are an increasing number in other atom's nuclei. It has the same magnitude of charge as an electron, though it is positive rather than negative.
Radioactive decay is a random process for individual atoms, but overall, a block of radioactive atoms' rate of decay is exponential, falling to zero eventually. The decay rate can not be affected by physical or chemical conditions. For a large number of atoms, the number of radioactive atoms will halve over a regular period of time, called the half life, and this results in the exponential nature.
Half life is the period of time (average, though accurate for a large number of atoms) required for the rate of decay of a radioactive sample to decrease to half its initial value. This is a constant for a given isotope.
The half life life can be determined from a graph by first taking a point on the graph, finding it's rate or decay. Calculate the rate of decay which is half of the original value, then find the point on the graph which corresponds to this half rate. The half life is the time (from the x-axis) between the two points.
The reactivity after n half lives will be Initial x (1/2)n. This equation is not in the data booklet, but is hopefully fairly obvious.