 
   Picture 5.2 A cathode ray tube.     Electron volts If we use an accelerating voltage of, say, 3 kV, this gives a kinetic energy of 4.8 x 10^{–16 }J. This is an extremely small number. For convenience, physicists use the unit of the electron.volt to measure energies of atomic and subatomic particles. Quite simply, the electrons gain a kinetic energy of 3 ke V. (i.e. 3 kilovolts multiplied by the charge on the electron). However, we do need the value in joules if we want to find their speed.      Thomson's start       Thomson generated a vapour of electrons by heating a metal wire. He then accelerated the electrons in a voltage to produce a beam, which made a spot on a fluorescent screen. He knew that the electrons must be negatively charged because they were repelled from the cathode and attracted to the anode. The electrons have their highest electrical potential energy (EPE) when they are by the cathode. As they move towards the anode, they lose electrical potential energy and gain kinetic energy. You can think of them as rolling down the hill of electrical potential energy. The electric field is doing work to accelerate them. We can find out how fast they are going using the conservation of energy: Electrical potential energy lost = kinetic energy gained  EPE lost = q V   where V is the potential difference (we will ignore the minus signs here – we know that negative electrons going from cathode to anode lose a positive amount of EPE).  also    KE = ^{1}/_{2} mv^{2}   assuming that the original evaporated electrons have negligeable KE     So:    4.8 x 10^{–16} = ^{1}/_{2} mv^{2}  v = (2 x 4.8 x 10^{16}/9.11 x 10^{31})^{1/2}  v = 3.24 x 10^{7} m.s^{1}      
   Picture 5.3 The air between the lectrodes can withstand a voltage of about 10 000 volts for each centimetre of the gap. Once the voltage gets bigger than this, there will be sparks and then the air will break down.        Relativistic effects – or not This is about a tenth of the speed of light. At this speed, there will be some relativistic changes to the electrons' mass. This means that, although the kinetic energy is still 4.8 x 10^{–16 }J, the speed will be slightly less than what we calculated. Luckily, as the electrons are not going too close to the speed of light, this didn't have too big an effect on Thomson's conclusions.         Turning up the voltage       By increasing the voltage, we can accelerate the electrons (and other particles) up to higher and higher energies. Unfortunately, if the electric field goes above a few thousand volts per cm the air between the electrodes breaks down and we get sparks (picture 5.3). So we cannot keep increasing the voltage to give the electrons one huge push. Instead, we have to give the electron a sequence of smaller pushes with manageable voltages. The simplest way to do this is in a linear accelerator.     
   Picture 5.4 The principle of a linear accelerator. A sequence of electrodes keeps on pusshing a beam of particles.      A simple linear accelerator       A linear accelerator is like a gun with a long straight barrel. In a linear accelerator, the electrons pass through a series of electrodes. If the electrons are to keep accelerating then they must always be leaving a negative electrode and heading towards a positive one. Therefore the voltages on the electrodes have to be switched over as the electrons pass through. Look at picture 5.4.  Electrode A is negative and B is positive so the electrons accelerate to the right.
 Before they pass out of B, it is made negative and C becomes positive to keep pulling them to the right.
 The voltage is switched back again to make D positive and C negative so they are pulled towards D.
The electrons are travelling close to the speed of light (300, 000 km.s^{1}). So the voltages have to be switched over very quickly. The frequency of the alternating voltage is a few hundred kilohertz (a radio frequency). Notice that electrode D is longer than electrode B. This is because the electrons are travelling faster by the time they reach D. So, if they are to spend the same time in D, it has to be longer. The longest linear accelerator is at Stanford in California in the USA. It is 3 km long and has an effective accelerating voltage of 30 GV (thirty thousand million volts). To get more acceleration would require even longer accelerators. Alternatively, the linear accelerator has to be bent around on itself. This kind of accelerator is called a synchrotron (see page 21).     
 


 