These notes are a "bare-bones"
summary of the material in the book.
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Electrostatic effects are seen when insulating objects like plastic are rubbed with a cloth and get a charge. They are charged by friction. There are two kinds of charge:
The charge comes from the electrons. Atoms have electrons (negative) orbiting the nucleus, which contains the protons (positive) and neutrons (no charge). If an electron is removed, the atom becomes a positively charged ion. If an electron is added, the atom becomes a negatively charged ion. Protons do not move.
Two important things to remember:
When you rub a polythene rod with a duster, electrons are transferred from the duster to the rod, making the rod negative. When you rub an acetate rod with the cloth, electrons are rubbed off the rod onto the duster, making the rod positive.
The Van der Graaff generator is static electricity generator that pumps electrons in large numbers to generate a very high voltage. If you put your hands on the machine, your hair will stand on end, because the like charges repel.
In general:
The most obvious hazard is an electrical shock. With static electricity, it is very small, so is not at all dangerous. A school Van der Graaff generator can generate 300 000 volts. A person touching it will only get a small shock; the same person touching a 25 000 volt overhead power line on the railway will be killed. It's not the voltage, but the current. The Van der Graaff generator produces no more than a couple of micro-amps (millionths of an amp). But:
The shocks cause ventricular fibrillation (a heart attack). If you are hot and sweaty, your body resistance is lower, so a lower voltage will give you a bad shock.
Other hazards include:
Static electricity can also be a nuisance rather than a hazard, attracting dust, or causing clothes to cling.
Hazards can be reduced by measures like:
The aeroplane below is being refuelled. You can see the bonding line by the nose-wheel.
These include:
The defibrillator is a machine that gives a controlled electric shock to the twitching heart of a heart attack patient. Two paddles are placed across the chest, and a large amount of energy (about 400 joules) is passed between the paddles from a high voltage supply. The patient convulses, but the heart is kicked back into action, thereby saving the patient's life.
If the 400 J shock takes 1 millisecond (0.001 s) the power (measured in watts)of the machine can be worked out:
Power (W) = energy (J) ÷ time (s)
Power = 400 J ÷ 0.001 s = 40 000 W
The defibrillators used by ambulance crews are large and require professional training. Smaller models have been developed for trained first aid personnel to provide immediate assistance. These can provide immediate help, which will help to reduce damage from the heart attack.
Implantable defibrillators can be installed in patients, which detect disturbances to the heart's electrical rhythms. They deliver a shock of about 20 J to get the heart working properly. When the batteries run down, the patient has to be opened up to get at it, which involves a little than undoing a few screws to open a cover...
Electrostatic dust precipitators help to keep the environment clean from soot that would otherwise come out of chimneys. They work like this:
For an electrical circuit to work:
When this happens, there is a current, which is a flow of charged particles, the electrons. Conventional current flows from positive to negative, while the electrons flow from negative to positive. (The early physicists got it wrong. By the time they discovered that it was too difficult to rewrite all the laws of physics!) We will regard all currents as conventional, i.e. flowing from positive to negative.
There are two electrical quantities that we can measure:
From these we can work out the resistance, measured in ohms (W). The strange looking letter is "Omega", a Greek capital letter long 'Ō'.
Here is a circuit to measure resistance.
Make sure you know what the symbols mean.
Voltage and current are proportional. That means if you double the voltage, you double the current. We can show this on a graph:
Resistance is worked out with the formula:
Resistance (W) = voltage (V) ÷ current (A)
In Physics Code:
R = V
I
The different rearrangements are:
V = IR
and
I = V
R
The physics code for current is I from the French, Intensité du courant.
When a current goes through a resistor, the electrons bump into the atoms of the resistor. The atoms vibrate more, so the resistor gets hotter. This makes collisions more likely, so the resistance goes up.
The filament in a light bulb has quite a low resistance when cold. It gets much higher when it glows, because it has got hot.
Mains electricity is supplied to our homes from a power station. It is alternating current (AC), in which the voltage and the direction is changing all the time.
We can see how alternating current is different to the direct current (DC) from a battery. The voltage is 230 V, while the electrons vibrate to-and-fro 50 times a second. We say that the frequency is 50 Hz.
Two wires connect the house:
The live that carries the supply;
The neutral that provides the return route to the power station.
There is also an earth wire that provides an alternative route to the substation through the ground. This is there for safety and there should be no current in it if the appliance is working properly. If a fault occurs the current should return to the ground safely, and blow the fuse.
A British pattern plug is wired like this:
The brown is connected to the live;
The blue is connected to the neutral;
The green and yellow wire is connected to the earth.
It is very important that plugs are wired properly, there are no bare wires showing and the cord grip is tight.
The fuse consists of 2 cm of very thin wire in a ceramic cartridge. It protects the appliance by melting if the current gets too big. A 5 A fuse will blow if the current gets more than 5 A.
The fuse will blow if there is a fault. The fuse is always in the live wire so that the appliance is isolated from the supply.
Look at this picture of a fault with a metal cased appliance.
A fault has occurred in which the live wire has become exposed and is touching the metal case. Since this appliance has only two-core cable, there is no earth wire. The appliance will work. However as soon as you touch it you will get a severe shock. The current involved in a shock (60 mA) will not blow the fuse, but may well kill you.
Now look what happens if there is three-core cable.
The earth wire is connected to the metal case of the appliance. The fault leads to a short circuit which will blow the fuse. The appliance will make a loud bang, but the case will not be live.
Earth leakage circuit breakers act as an extra safety device if you are using electrical appliances outside, for example an electric lawnmower.
Many appliances have plastic cases. Metal parts are not accessible in normal use. Therefore there is no need for an earth wire and they are connected by a two core cable. These appliances are called double insulated. The symbol for a double insulated appliance is shown below.
Every house has a fuse-box where there are fuses to protect the circuits in a house. Modern houses have circuit breakers that trip if there is a fault. These can be reset once the fault has been repaired.
The range of human hearing is from 20 Hz to 20 000 Hz (20 kHz). The ear is most sensitive to 3000 Hz. A sound wave is a longitudinal wave, caused by vibrating particles. The particles vibrate parallel to the direction of the wave, while for a transverse wave, the particles move at right angles to the direction of movement.
Like all waves, sound waves have:
an amplitude - the maximum displacement from the rest position. This corresponds to the volume;
a wavelength - the distance between two compressions;
a frequency - this is the number of waves per second, corresponding to the pitch.
The sound wave consists of:
Compressions - regions of high pressure;
Rarefactions - regions of low pressure.
Sound waves are mechanical waves. They need a material to travel in. They cannot travel in a vacuum. Common values for the speeds for sound are:
330 m/s in air;
1500 m/s in water;
5000 m/s in steel.
You can see that the closer atoms are together, the faster the sound is.
In Ultrasound scans the sound waves are reflected as echoes from the boundaries of body tissues. As well as looking at unborn children, these scans can be used to diagnose other illnesses. They can also detect the flow of blood in a blood vessel.
Other uses include:
breaking up kidney stones;
removing scale off teeth;
cataract surgery.
It is important for good sonic contact that a gel is used between the probe and the skin.
As the sound is reflected off different boundaries (interfaces) the depth can be calculated with the speed equation:
distance = speed × time.
There are standard speeds of sound in tissues. The proportion of ultrasound reflected depends on:
The densities of neighbouring tissues - if they are of greatly differing densities, the waves are reflected. Few penetrate further.
The speed of the sound in the adjoining tissues.
Ultrasonic monitoring of moving tissues (e.g. blood, or a heart) uses the Doppler effect, which changes the frequency of the echoes.
Ultrasound is less damaging to tissues than X-rays. It also distinguishes much better between soft tissues. X-rays are good for shadow pictures of bones.
X-rays and Gamma rays are used widely in diagnosis (finding out what is wrong with the patient) and therapy (treating the patient so that they get better). They are both:
electromagnetic waves with very short wavelengths;
very penetrating, passing deep into the body, or even through it;
potentially risky - care must be taken not to expose the body to too much of them.
Note that the boundary between X-rays and Gamma rays is not distinct. We can talk of hard X-rays which are more energetic than gamma rays.
X-rays are produced in an X-ray tube by accelerating electrons with a high voltage towards a tungsten target. The tungsten atoms are hit by the electrons which have a high kinetic energy. They get very energetic (excited) and release X-rays, getting rid of their surplus energy. Most of the kinetic energy is lost as heat, so the tube is not very efficient.
The differences between X-rays and Gamma rays are that:
You can control the rate of production of X-rays from a tube. You cannot control the rate from a radioactive source.
Gamma rays have a particular energy that entirely depends on the radioactive material. The energy from X-rays can be changed.
X-rays come from the electron shells around atoms; gamma rays come from within the nucleus.
People working with any kind of radiation need to wear a film badge to monitor their exposure to radiation. If it gets too high, then they cannot work with radiation.
In hospitals radiographers carry out procedures that involve gamma and X-ray radiation. The most commonly used source is Cobalt-60, a radioactive isotope of cobalt. Both kinds of radiation can be used for treatment as well as diagnosis. Radiotherapy involves carefully lining up sources of X-rays or gamma rays at a cancer. They destroy the cancer cells. Side-effects can be unpleasant.
Gamma radiation. can be used to sterilise hospital equipment, especially that which can't be sterilised by heating with steam (e.g. some plastic items)
Tracers are used to diagnose illnesses, which avoids the need for surgery. Both technetium-99 and iodine-123 are radioactive isotopes that emit gamma rays. They can be taken orally or injected. The movement of the tracer is monitored using a gamma camera. X-rays are not suitable as they are generated in an X-ray tube.
One of the problems with using gamma rays to treat cancers is that the dose from a single source that would kill a cancer would also kill healthy tissue. This problem can be minimised by having several sources giving out radiation accurately pointed at the tumour. The sources are rotated so that the healthy tissue only gets intermittent short doses of radiation, while the tumour gets the lot.
Tracers should be short-lived; you don't want the muck slopping about your body for longer than you need. A cobalt 60 source needs to be long lasting; you don't want to be replacing it every other day.
Some isotopes of elements have unstable nuclei with too many neutrons which break up in particular ways to emit radiation. They are called radioisotopes. There are three kinds of radiation:
| Radiation | Ionising Power | Range in air | Stopped by | What is it? |
| Alpha | Very strong | About 5 - 10 cm | Paper or skin | Helium nucleus |
| Beta | Medium | About 1 m | 3 mm aluminium | High speed electron |
| Gamma | Weak | Infinite, but intensity reduces with distance | Reduced by thick lead | Electromagnetic radiation |
Note that:
They are called ionising radiations because they can knock electrons off atoms.
Alpha emitters are safe to have around as the particles are stopped by skin. Inside the body they will destroy cells very quickly causing radiation sickness. They are not used for radiotherapy or diagnosis.
Beta emitters are used occasionally in some treatments.
Gamma rays penetrate a long way. They can come out of the body as well as go in.
An alpha particle is a helium nucleus,
NOT a helium atom.
We can detect the ionising radiation with a Geiger-Müller tube. If it's connected to a counter, we can count the number of disintegrations per second. The count rate is measured in counts per second or becquerels (Bq). The formula is:
count rate (Bq) = number of nuclei that decay
time in seconds
The process of decay is entirely random. It cannot be increased by heating the radioisotope, or hitting it, or reacting it with other reactive chemicals.
The rate of radioactive decay:
is different for different elements;
depends on the number of nuclei that are present.
Let us suppose that we measure the count rate over a period of several days. The initial rate we measure as 100 %. After 2 days we find that the count rate has fallen to 50 %. After 4 days it has not dropped to 0, but to 25 %. After 6 days it is 12.5 %. After 8 days it's 6.25 %.
Every 2 days the activity has fallen to half what it was 2 days before. We call this period the half-life. It's a property of the element and does NOT change. On a graph the decay looks like this:
This graph is called an exponential decay. In theory the activity never gets to 0, but after several half-lives, it's very low. Half lives of radioisotopes vary from tiny fractions of a second to many hundreds of millions of years.
Radioactive Decay Equations
Any nucleus can be described like this:
A is the nucleon number (the number of both protons and neutrons). In some texts it's the mass number.
Z is the proton number. In some texts it's the atomic number.
The number of neutrons can easily be worked out:
Neutrons = A - Z
For example Polonium-210:
There are 210 nucleons of which 84 are protons. Therefore:
number of neutrons = 210 - 84 = 126
For Alpha decay we get:
When an alpha particle is emitted:
The proton number goes down by 2;
The nucleon number goes down by 4.
Since the proton number has changed, the element has changed. Note that nucleons are never lost; they all have to be accounted for.
After the emission the nuclei are still excited and get rid of excess energy with a gamma ray.
For Beta decay we get a neutron turning into a proton:
When a beta particle is emitted:
the proton number goes up by 1;
the nucleon number stays the same;
a high speed electron travelling at 1/10th the speed of light (3 × 107 m/s) is given off;
a tiny little particle called an electron antineutrino is also given off.
There is always a certain level of ionising radiation in the environment. This background radiation comes from:
Radioactive elements in rocks, soil, and bricks;
Cosmic rays from space;
Human sources, about 1 %, such as nuclear waste from hospitals and the nuclear power industry, and artificial radioisotopes.
When we do an experiment with radioactive sources, we must take the background radiation into account when measuring count rates:
True count = count on the counter - background count
The smoke detector has a weak alpha source that sends alpha particles between two charged plates The alpha particles ionise the air, allowing it to conduct a tiny current. If there are smoke particles, the ionised air molecules attach to these, reducing the current. This is sensed and the alarm is sounded.
The alpha source is Americium-241, which has a half-life of about 28 years. This means that the alarm does not have to be replaced so often.
Tracers
These are gamma emitting radioisotopes that can be used to trace underground pipes and leaks in them.
Gamma has to be used, as it's the only radiation that penetrates several metres of ground;
The radioisotopes need to have a short half-life, as you don't want the radioactive waste hanging around for longer that necessary.
The tracer is introduced into the pipe and a detector is used to trace the course of the pipe. When there is a leak the radioisotope pools and a strong signal is given out. Downstream of this point, the activity drops off. So engineers can be confident of the area in which to dig - once the gamma radiation has decayed.
Some rocks have uranium in them. Uranium decays with a half-life of 4500 million years through a a series of other elements eventually to form lead. We can look at the proportion of lead to uranium, and work out how many half-lives the uranium has undergone.
Uranium decays by alpha decay to thorium. Then thorium decays by beta decay to protactinium. There are a number of short-lived intermediates until lead is formed. Lead is the most massive of the stable elements; it has the highest proton number and the highest nucleon number. Any element of isotope that is higher than a nucleon number of 206 and a proton number of 92 is unstable. If the proportions are equal, then the rock must be 4500 million years old.
Uranium 235 decays by alpha decay, but has a half-life of 700 million years. It can be used to date younger rocks.
Biological materials can be dated using carbon 14 which decays to nitrogen. Looking at how much carbon 14 is left in a biological relic and comparing it with how much is present today, we can estimate the age of the material.
Carbon 14 is formed when high energy cosmic rays knock out neutrons from other nuclei. They are picked up by nitrogen atoms. One of the protons in the nitrogen nucleus turns into a neutron, by a kind of reverse beta decay (we won't go into that here).
Living things pick up carbon-14 naturally. It is present in a ratio of 1 carbon-14 : 1012 carbon-12. The level stays roughly constant while the organism is alive. When it dies, the carbon-14 is no longer absorbed, so it starts to decay by beta decay:
The half-life is about 5700 years. So very old biological materials cannot be dated this way because the carbon-14 has decayed to insignificant levels.
Uranium -235 decays by alpha decay with a half-life of 700 million years. However when a neutron is added to the nucleus, the nucleus becomes highly unstable and splits into new elements, giving off a further three neutrons and a lot of energy. This process this called fission.
Radioactive decay is NOT the same as fission.
Nor is fusion. And there's no such thing as fussion!
The neutron has to be of the right speed:
too fast, it goes right through the nucleus;
too slow and it will bounce off.
Neutrons of the right speed will be captured by the nucleus. It is important to understand that the nucleus is not a neat little ball of protons and neutrons; it is bedlam. It is better to think of the nucleus as a "wobbly drop", which is NOT smashed by the neutron. To be unscientific, it is "tickled" by the neutron and "laughs" itself to bits. If you want that in more scientific terms, the neutron is captured, and the nucleus is so unstable it comes apart.
A lot of energy is released, along with, on average, 3 more neutrons. These in turn are captured by other nuclei, which in turn split, each to give 3 more neutrons, making 9 in all. Then 27. Then 81... This is called a chain reaction.
To increase the chances of a self-sustaining chain reaction, there has to be a certain amount of fissile material. This is called the critical mass. For uranium it's about the size of a tennis ball.