Electron
Quantum and Nuclear

Properties of the electron

for 14-16

Physicists currently think that the electron is a fundamental particle. As with any particle at this scale, it can only be defined by its properties. Some of these properties can be measured in the school laboratory.

There is enormous benefit to intermediate and advanced students of seeing some of these experiments. They give an authentic experience of some major developments in particle physics and, in the case of electron diffraction, a glimpse into the counter-intuitive and exciting world of quantum objects.

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Perrin tube – sign of electron charge

Electron
Quantum and Nuclear

Perrin tube – sign of electron charge

Practical Activity for 14-16

Demonstration

This experiment, conducted by Perrin in 1895, was crucial in the very early studies of electron beams.

Apparatus and Materials

  • Perrin tube and stand
  • Coils for deflecting beam, 1 pair
  • Power supply, 0–5 kV (Extra High Tension, EHT)
  • Low voltage supply (6 volt) for heating filament (this is often included on the EHT supply)
  • Gold-leaf electroscope
  • Power supply, low voltage, variable, 0 - 12 V
  • OR
  • Battery pack, 6V, 2
  • Rheostat
  • Switch, 1
  • Helmholtz coils

Health & Safety and Technical Notes

Use an EHT supply of no more than 5 kV, which is current limited to less than 5 mA.

The power supply for the heater MUST have adequate insulation.

Leads used MUST have shrouded connectors and insulation capable of withstanding 5 kV.

Make all connections with the power supply turned off. Do not adjust connections while the EHT is switched on.

Electron beam tubes are fragile. Because they are evacuated, they will implode if they break. The tubes are also expensive, so handle them with great care. Use the purpose-designed holders during practical work.

Note that when switching the EHT supply off, it can take a little while for the voltage output from the EHT to fall to zero. Allow sufficient time before disconnecting.

Read our standard health & safety guidance


Follow the manufacturer’s instructions for setting up the tube.

Ensure that you can identify the following:

  • The 6.3 V supply to the cathode heater (if you connect the wrong voltage to the heater you can easily damage the tube beyond repair).
  • The EHT supply to the electrode. Set this to zero.
  • The collection plate and its connection terminal in the Perrin tube

Use a proof plane (a small insulated metal plate) to test the sign of the charge on the electroscope. Use the plane to transfer charge from the power supply to the electroscope. To transfer negative charge, earth the positive terminal and touch the plate with a lead from the negative terminal. To transfer positive charge, earth the negative terminal and touch the plate with a lead from the positive terminal.

Make sure the glass envelope is clean and dry. You can wash it in methylated spirits and dry it in warm air.

A Faraday cylinder is contained within the tube at about 45 degrees to the axis of the undeflected beam. The magnetic field is adjusted so that the beam enters the cylinder. If the cylinder is connected to a gold-leaf electroscope, there will be an immediate rise in potential.

Procedure

Setting up:

  1. Set up the Perrin tube in its special stand.
  2. Set up the coils – one on each side of the tube. Connect them in series with each other and with the 12-volt power supply (or battery, rheostat and the switch). Set the current in the coils as low as it will go and leave the coils switched off for now.
  3. Connect the gold leaf terminal of the electroscope to the terminal on the Faraday cylinder.
  4. Connect the 6.3 V supply to the filament. (Some EHT supplies available for school use incorporate this output.)
  5. Connect the negative terminal of the EHT supply to the filament and the positive terminal to the anode.
  6. Carrying out:
  7. Set the EHT voltage to zero and switch on the 6.3 V supply to the heater filament.
  8. Increase the voltage of the EHT supply. At about 3 kV, the electron gun produces a narrow circular beam of electrons which passes through the hole in the anode. You should be able to see a spot about 4 mm in diameter on the screen at the end of the tube.
  9. Switch on the coils circuit. Use the rheostat to steadily increase the current. The spot on the screen should be deflected more and more as the current in the coils increases.
  10. Increase the current until the beam is deflected into the Faraday cylinder. The charge is collected and it will produce an immediate deflection of the gold leaf in the electroscope.
  11. To test the nature of the charge deposited, the best arrangement is to use an insulated proof plane. Stand the proof plane on a sheet of paper, which itself lies on the bench. Momentarily touch the plane with a negatively charged rod e.g. by friction charging a piece of polythene. This will provide the plate with a considerable negative charge. Then use the plane to test the sign of the charge on the electroscope. (The gold leaf will fall.)

Teaching Notes

  • The stream of electrons is deflected into a Faraday cage, which is connected to an electroscope, to show that electrons have a negative charge.
  • It is important that the whole beam should enter the cylinder to avoid the production of secondary electrons by the beam striking the sides. For this reason it is more reliable to use the coils to deflect the beam than to do the experiment with a bar magnet deflecting the beam.
  • You may find that the charge leaks away as soon as you remove the magnetic field that is causing the deflection. To prevent this happening, keep the lead from the Perrin tube to the electroscope as short as possible and avoid any sharp projections.

This experiment was safety-tested in March 2008

Up next

Measuring e/m

Electron
Quantum and Nuclear

Measuring e/m

Practical Activity for 14-16

Demonstration

This experiment shows that a cathode ray is made up of particles with a constant ratio of charge to mass ( e/m ). A magnetic field bends the cathode rays into a closed circle.

Apparatus and Materials

  • Fine beam tube and stand
  • Power supply, 0-250 V (High Tension, HT), with special shrouded connecting leads
  • 6.3 V supply for the heater filament (this is often included on the EHT supply)
  • Demonstration meters, 2
  • DC dial: 5 amp
  • DC dial: 300 volts
  • Hall probe
  • Helmholtz coils
  • Power supply, low voltage, variable, 0 - 12 V
  • OR Battery pack, 6V, 2 & Rheostat

Health & Safety and Technical Notes

Make all connections with the power supply off.

Connecting leads used for the HT voltages must have adequate insulation.

The HT supply can deliver a fatal current. Use 4 mm leads with plugs having sprung shrouds for all high-voltage connections. The teacher supervising in a darkened room must be aware of the hazards and their control.

Do not connect or disconnect leads once the HT is switched on.

Read our standard health & safety guidance


The simplest way to measure the magnetic field strength is to use a Hall probe. These are available from most equipment manufacturers. They come as a stand-alone unit which gives a digital read-out of magnetic field strength.

Hall probe sensors are also available with some computer interfaces – as one of the sensors that plugs into the interface. If you already have one of these interface kits, this might be a cheaper option than a stand-alone Hall probe.

For this experiment, students don’t necessarily need to know how the Hall probe works – you can introduce it simply as a device for measuring magnetic field strength.

A Teltron-type tube works best for this demonstration because you can use the electron gun that sends out a vertical beam. This can then be bent into a complete circle.

Follow the manufacturer’s instructions for setting up the fine beam tube.

Ensure that you can identify the following:

  • The 6.3 V supply to the cathode heater (if you connect the wrong voltage to the heater you can easily damage the tube beyond repair).
  • The HT supply to the anode. Set this to zero. The negative terminal of the HT goes to a socket, which is often near to the heater terminals.

A tube which has not been used for a while may not emit electrons. It may be possible to encourage it to do so by increasing the heater voltage by around 1 V or so. Monitor it carefully. Ensure that the normal heater current is only slightly exceeded.

Procedure

Setting up...

  1. It is best to measure the magnetic field from the coils before setting up the tube. Set up the coils without the fine beam tube – one on each side of where the tube will be. Connect them in series with each other, with the ammeter and with the 12-volt power supply (or battery, rheostat and the switch).
  2. Set the current in the coils to about 2.5 amps.
  3. Use the Hall probe to measure the magnetic field.
  4. Switch the coils off for now. Do not adjust the rheostat or power supply from now on.
  5. Set up the fine beam tube in its special stand.
  6. Select the gun which gives a vertical electron beam. (There may be a selection switch.)
  7. Connect the 6.3 V supply to the filament. (Some HT supplies available for school use incorporate this output. Alternatively, it is possible to use a separate low voltage transformer.)
  8. Connect the negative terminal of the HT supply to the filament and the positive terminal to the anode.
  9. Connect a voltmeter between the anode and cathode in order to measure the accelerating voltage, which should be about 250 volts.
  10. Carrying out...
  11. Set the HT voltage to zero and switch on the 6.3 V supply to the heater filament.
  12. When the filament is glowing, carefully increase the anode voltage. At a voltage, which may be as low as 50 volts, it should be possible to see the fine beam. As the voltage is slowly increased, the beam will lengthen and strike the glass envelope of the tube.
  13. Switch on the current to the coils. The beam should be bent into a circular path.
  14. Adjust the accelerating voltage until the beam forms a complete circle inside the tube – coming back around on itself. (Do not change the current in the coils unless you really have to. If you do change it, you will need to measure the field again).
  15. Increasing and decreasing the accelerating voltage on the electron gun will show how the radius of the path of the electrons varies with the speed of the electrons for a constant magnetic field. The faster the electrons, the more difficult they are to bend, so the radius of the path increases.
  16. Each group of pupils should measure the path diameter D and the accelerating voltage. To measure D, simply hold a ruler outside the tube. In the darkened room, the ruler should be illuminated. (A Perspex ruler with a small electric lamp taped to one end - and covered with masking tape so that no direct light emerges – works well.)
  17. Increasing the current through the field coils for a constant voltage on the electron gun will show how the circular path of the electrons changes with the strength of the magnetic field. The stronger the magnetic field, the more effect it has on the electrons and the circular path reduces in radius. If you change the current in the field coils, be sure you return it to the value at which you measured the field strength.

Teaching Notes

  • This experiment is best demonstrated to the students in groups of four to five in a darkened room if full value is to be obtained.
  • Always reduce the anode voltage to zero when not actually observing the beam because the tube has a finite life time.
  • The electron beam is visible because there is a low-pressure gas in the tube. Electrons striking the gas molecules transfer energy; the molecules then emit light. Hydrogen gas glows blue and helium gas glows green.
  • It is worth reminding students of the catapult field on a current carrying wire before showing the deflection of electrons. (See Related Experiments, below.) In the case of the magnetic force on a beam of electrons we must change the expression from the force of a magnetic field on a current carrying wire into the force of a magnetic field on a moving charge. Given that the beam is made of electrons, the direction of the current is towards the cathode.
    • The force F on a wire of length L carrying current I in a magnetic field B is F = ILB.
    • Here I = e / t and v = L / t, where e is the electron charge and v is its speed.
    • So F = evB
  • In the fine-beam tube the catapult force of the magnetic field is perpendicular to the stream of negatively charged electrons and so a uniform magnetic field will hold the stream in a circular orbit provided the electrons move at a constant speed. The magnetic field pulls the electrons into an orbit rather like a tether that holds a whirling ball.
  • If the tube is twisted slightly in its holder then the circular motion of the beam combines with a linear component of the beam to make a spiral.
  • It is helpful if students practise measuring the diameter of the beam by measuring the diameter of a wire loop without being allowed to bring the wire loop near to the rule. Practice with the loop will save time when they all measure the beam diameter.
  • The best modification so far produced forms a virtual image of an illuminated scale inside the tube, in the plane of the electron stream. To do this, place a vertical sheet of clean plate glass just in front of the tube. Place an illuminated scale in front of the sheet at such a distance that the image of the scale, behind the sheet, is in the middle of the tube. This does make measurements easier; but we do not recommend adding this complication except with a very able group.
  • The emphasis is to bring students into contact with real experiments on electrons and not to worry too much about precision, which may be beyond the design of the apparatus. Students should be encouraged to devise refinements, such as measuring the diameter of the electron beam, but too many refinements will make the experiments very complicated and the simple elegance of it will be lost.
  • When JJ Thomson measured the value of e/m he did not have the luxury of a heated cathode producing electrons all at the same speed, and so he did not know the speed of the electrons. He had to deflect his beam of electrons with a magnetic field and then return them to their undeflected position with an electric field.
  • It is worth discussing with students what they can infer from this experiment (and what they can’t).
    • The fact that the cathode rays are deflected shows that they have charge; the direction of the deflection shows the charge is negative (which was already assumed because they emerged from a cathode).
    • The fact that they are deflected in a curved path and not deflected through a right angle shows that they have inertia or mass. From this, we assume that the cathode ray is made up of particles.
    • The fact that the whole beam is kept intact shows that the particles are all deflected by the same amount.
    • It is likely that the beam is made up of particles that are all the same. But, at this stage, we cannot infer this for certain.
    • We can infer that the ratio of the charge to mass of all the particles is the same. If there are some particles in the beam that have twice the charge, they must also have twice the mass. This is because they all follow the same orbit; the radius of the orbit depends on the acceleration. In turn, the acceleration depends on the force on the particles and their mass. The doubled charge will cause the force to be twice as big but the doubled mass will mean that the acceleration is the same.
  • Using the results to find e/m (the specific charge):
    • The electrons are accelerated in an electric field. Increasing the accelerating voltage increases the speed of the electrons. Energy that was stored in the electric field (electric potential energy) is now stored kinetically. So
    • Increase in kinetic energy = decrease in electrical potential energy
    • 1/2 mv2 = e V (equation 1) where m is the mass of the electron, e its charge, v its velocity and V the accelerating voltage
    • These moving electrons enter the magnetic field produced by the coils. This bends them into a circular orbit.
    • The magnetic force, F , on the electrons is given by
    • F = B e v where B is the magnetic field strength, e is the charge on the electron and v their speed
    • Given that the electrons are going in a circle, we know that this force must have a size of
    • mv2 / r where m is the mass of the electron and r is the radius of the orbit.
    • So you can say that:
    • B e v = mv2/ r
    • so B e = mv / r (equation 2)
    • There are two ways you could use these equations with students. The first is algebraic and the second uses values for the speed. The first is more complete. However, you might want to use the second so as not to distract students from the accomplishment of measuring properties of the electron.
  • Algebraic approach:
    • Combining equations 1 and 2 will lead to the equation:
    • e/m = 2V/B2r2 from which students could calculate values of e/m
    • or r2 = 2Vm/eB2 from which students could plot a graph of r2 against V and find e/m from the gradient.
  • Using values for speed:
    • A simple rearrangement of equation 2 gives,
    • r = mv/Be
    • So a graph of r (radius) against v (speed) will yield a value for e/m. However, you cannot calculate the speed from equation 1 (without independently knowing e/m). However, you can use the table below to give students the (non-relativistic) speeds at different voltages. These are correct to within 1%.
  • Gun Voltage/VSpeed of Electrons/m/s
    1006 × 106 
    1408 × 106 
    1808 × 106 
    2309 × 106 
    28510 × 106 
  • The accepted value of e/m is 1.76 x 1011 C/kg.
  • You will do well to get a result that is the correct order of magnitude. There are quite large uncertainties in the radius measurements and some uncertainty in the measurement of the magnetic field strength. Both of these quantities are squared in the algebraic method.
  • Knowing that the charge on an electron, e = 1.6 x 10-19 Coulomb from Millikan’s experiment, together with the value for e / m = 1.76 x 1011 C/kg leads to a value of 9 x 10-31 kg for the mass of the electron. The same value of e / m is found for all electrons, whatever their source – hot filaments of metals, the photoelectric effect, bombarding gases by electrons, electric fields tearing atoms apart and even nuclei emitting beta particles. This evidence leads scientists to suppose that electrons are universal ingredients of matter, all identical.
  • A similar calculation for the proton, with charge e = 1.6 x 10-19 Coulomb and e / M = 9.6 x 107C/kg leads to a value of 1.67 x 10-27 kg for the mass of a proton.

This experiment was safety checked in March 2008

Up next

Preparation for Millikan’s experiment (dancing men)

Electron
Quantum and Nuclear

Preparation for Millikan’s experiment

Practical Activity for 14-16

Demonstration

This demonstration shows that charged particles will be attracted up or down when placed between parallel charged plates. It also shows that the electric field can support the weight of the charged particle between the plates. It might already have been shown when discussing how capacitors behave.

Apparatus and Materials

  • Large metal plates, 2
  • Power supply, 0 – 5 kV (Extra High Tension, EHT)
  • Aluminium leaf
  • Scissors
  • Pillars of insulator, 3

Health & Safety and Technical Notes

Use an EHT supply of no more than 5 kV, which is current limited to less than 5 mA..

The power supply for the heater MUST have adequate insulation.

Leads used MUST have shrouded connectors and insulation capable of withstanding 5 kV.

Make all connections with the power supply turned off. Do not adjust connections while the EHT is switched on.

Electron beam tubes are fragile. Because they are evacuated, they will implode if they break. The tubes are also expensive, so handle them with great care. Use the purpose-designed holders during practical work.

Note that when switching the EHT supply off, it can take a little while for the voltage output from the EHT to fall to zero. Allow sufficient time before disconnecting.

Be careful not to accidently touch the plates.

Read our standard health & safety guidance


In effect, you are building a parallel plate capacitor. The top plate becomes positively charged and the bottom one negatively charged. There is a uniform electric field between the plates.

When one of the pieces of metal foil touches a plate then it becomes charged by sharing charges with the plate. It is then repelled by the charge on that plate and attracted to the opposite charge on the other plate. The charging process repeats and the pieces of foil bounce up and down.

The EHT has a floating earth so you can make the top plate positive or negative. However, we have assumed here that it will be positive. The experiment will work the other way but making the top plate positive is more like the Millikan experiment because it will exert an upwards force on negative charges (like Millikan’s charged oil drops).

Procedure

    Setting up...
  1. Place one metal plate on the table and connect it to earth.
  2. Use the insulating pillars to support the other plate about 10 cm above the earthed plate, horizontal and insulated.
  3. Cut or tear from the book some small scraps (1 cm) of metal leaf. (Or cut them in the shape of small men, say 2.5 cm high.)
  4. Carrying out...
  5. Connect the two plates to the EHT supply to establish a vertical electric field in the space between them. With the EHT switched off, connect the top plate to the positive terminal of the EHT and the bottom (earthed) plate to the negative.
  6. Place the scraps of leaf in the space between the plates. Then the scraps acquire charges when they touch either plate and are driven to the other plate; so they dance up and down in the space between the plates.
  7. To show that the electrostatic charges will maintain a similar dance, replace the upper plate by a sheet of plastic. Charge the plastic by rubbing.

Teaching Notes

  • The Millikan experiment is very fiddly and so not generally done at school level. However, it is an experiment of great historic value because it produced a value for the charge on the electron and showed that electrons are discrete particles, each carrying the same charge.
  • In Millikan’s experiment the apparatus is much smaller and the ‘dancing men’ are replaced by a tiny drop of oil (or in new models a tiny bead of plastic) which is allowed to gain a few extra electron charges. That tiny drop falls slowly, delayed by air resistance, and it rises slowly when the plates are suitably charged. The plate charges can be adjusted by changing the potential difference across the plates to hold the tiny drop at rest, floating in the air. Then the charge on the drop can be calculated.

This experiment was safety-tested in March 2008

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A model of Millikan’s experiment

Electron
Quantum and Nuclear | Electricity and Magnetism

A model of Millikan’s experiment

Practical Activity for 14-16

Demonstration

A qualitative experiment to show the principle of a force on a charged body between two parallel plates.

Apparatus and Materials

  • Macro-Millikan apparatus
  • Power supply, 0–5 kV (Extra High Tension, EHT)
  • Proof plane
  • Polythene tile
  • Charging cloth

Health & Safety and Technical Notes

Use an EHT supply of no more than 5 kV, which is current-limited to less than 5 mA.. The power supply for the heater MUST have adequate insulation. Leads used MUST have shrouded connectors and insulation capable of withstanding 5 kV.

Make all connections with the power supply turned off. Do not adjust connections while the EHT is switched on.

Electron beam tubes are fragile. Because they are evacuated, they will implode if they break. The tubes are also expensive, so handle them with great care. Use the purpose-designed holders during practical work.

Note that when switching the EHT supply off, it can take a little while for the voltage output from the EHT to fall to zero. Allow sufficient time before disconnecting.

Be Careful not to touch the exposed plates.

Read our standard health & safety guidance


The illustrations show the ‘macro-Millikan’ apparatus. It consists of a pair of metal plates, one of which has a central hole through which a small polystyrene ball can pass. The ball has a length of nylon thread attached, and at the other end of the thread is a Pyrex glass spring.

The best arrangement for securing the upper end of the spring is to attach it to another loop in a nylon thread. This is taken up over a pulley connected to the ceiling, and then to an eyelet on a block of wood. Alternatively, a support from a long retort stand rod can be used, as shown below, and brought up over the plates, forming a hooked support.

Procedure

  1. With the EHT switched off, set the plates up horizontally, 7 to 10 cm apart, one above the other.
  2. Connect the earth terminal of the power supply to its negative terminal. Connect the lower plate to the earth terminal of the EHT power supply. Connect the upper plate to the positive terminal. To reverse the field, change the leads to the supply, but in each case the lower plate should be earthed.
  3. Lower the small conducting sphere with its nylon suspension through the hole in the upper plate. The upper end of the nylon suspension is looped and connected to the Pyrex glass spring.
  4. Rub the polythene tile and put the proof plane on it, touching to charge the proof plane by induction. Without making contact with the plates, bring the proof plane up to the conducting sphere to charge it by contact. Adjust the suspension so that the sphere is almost exactly half-way between the two plates. This is most conveniently done in the first arrangement described above. By moving the block of wood nearer to or away from the apparatus, the sphere can be lowered or raised.
  5. Switch on the EHT supply, set at 2 - 4 kV. The sphere will move as the extra force stretches the spring. The sphere can be brought back to the central position by moving the block of wood. Students will see the movement quite clearly if their eyes are in line with the plates.

Teaching Notes

  • There are no measurements to be made in this demonstration: it is a qualitative experiment to show the principle of a force on a charged body between two parallel plates. Quantitative experiments do not lead to very satisfactory results unless considerable trouble is taken. There is a tendency for the charge to leak away along the suspension.
  • If the ball is near one plate, the charge on it induces an opposite charge on that plate, so there is attraction. You do not want that ‘image-force’ to appear in the demonstration. The ball must be almost exactly half-way between the two plates, so that the image forces cancel out.
  • Students' eyes need to be in line with the plates. It is easier to see the movement of the ball if a plane mirror is placed behind the suspension with a horizontal line ruled across it, whilst a small cardboard disc is attached to the nylon suspension to act as a pointer. This pointer is aligned with the mark on the mirror before the field is switched on, but after the sphere has been positioned at the centre of the plate. However, this special arrangement may divert attention from the general idea and need not be used in this qualitative demonstration.
  • You may like to experiment with a realistic model of the Millikan experiment. Place a very light metal-coated ball in the field between the plates. Adjust the field to make the ball float upwards, fall slowly downwards, or even remain poised at rest for a short time. The ball is charged by contact with one of the plates, which then repels it. A very light ball is needed, or perhaps a scrap of aluminium leaf. When the ball is poised, its equilibrium is made unstable by image forces. To minimize that disadvantage, the charge on the ball should be made as small as possible and the electric field as large as possible.

This experiment was safety-tested in March 2008

Up next

Millikan's method for money

Electron
Quantum and Nuclear

Millikan's method for money

Practical Activity for 14-16

Demonstration

In this demonstration, students find the mass of a single coin by measuring handfuls of coins. The mass of a single coin represents the basic unit of charge. The handfuls represent the charge on an oil drop.

Apparatus and Materials

  • Box of coins or dice or plastic tokens (50 or more – the more, the better)
  • Scales, preferably digital
  • Beaker, large plastic, 2

Health & Safety and Technical Notes

Read our standard health & safety guidance


To avoid any problem of coins being pocketed by students, it is best to use coins that are not in circulation as money i.e. use foreign or old coins.

There are many alternatives to coins. Coins are good because they all have the same mass. And the mass is fairly big (so any variation in mass is insignificant). However, you can use dice, tokens, tiddlywinks or many other alternatives as long as their masses are similar.

Make sure all the coins are similar.

Make sure you know the mass of the whole collection of coins (to ensure you have them all back at the end).

Procedure

  1. Put an empty beaker on the balance and set the reading to zero.
  2. Take the beaker off and pour or drop in a handful of coins. It is best not to do this on the balance because you might damage the balance with the force from the falling coins.
  3. Measure the mass and record it so that all students can see it.
  4. Remove the beaker and remove all the coins. Put in another handful. Measure and record its mass.
  5. Take as many readings as you think are needed for students to be able to calculate the mass of a single coin by finding the highest common factor.
  6. Ask the students to find the highest common factor from the masses of handfuls that are on the board. A good place for them to start is to subtract values that look close together.

Teaching Notes

  • One of the key ideas in Millikan’s oil drop experiment is the use of the ‘highest common factor’ to find the charge on a single electron. In 1910 Robert Millikan measured the charge on a number of oil drops. He reasoned that, each time, the charge on the drop was made up of whole number multiples of a basic unit charge. He found this basic unit of charge by looking for the highest common factor that could be multiplied up to give the charge on each oil drop that he measured.
  • In this demonstration, students find the mass of a single coin by measuring handfuls of coins. The mass of a single coin represents the basic unit of charge. The handfuls represent the charge on an oil drop. The handfuls are always sufficiently big that you can’t see how many coins are there. After a number of measurements, students can find the highest common factor to deduce the mass of a single coin.
  • It is worth the teacher knowing beforehand what the mass of a single coin is.
  • It is best not to add or take away coins from the beaker. This is because it will be clear to perceptive students how many coins you added or took away. Nevertheless, it is worth helping the students by trying to get a few readings with fairly similar number of coins.
  • You could discuss the way that Millikan rejected some numbers from his results because they didn’t fit with his ideas on what the charge should be. You could model this by privately using a calculator to see if any of the measurements are not exact multiples of the mass of a single coin. Any that aren’t, you could either change or delete. Discuss whether this is good scientific experimental technique.

This experiment was safety-tested in March 2008

Up next

Electron diffraction

Bohr Model
Quantum and Nuclear

Electron diffraction

Practical Activity for 14-16

Demonstration

Visible diffraction rings on a screen show the wave behaviour of electrons.

Apparatus and Materials

  • Electron diffraction tube
  • Power supply, 0 - 5 kV (Extra High Tension, EHT)

Health & Safety and Technical Notes

For use with a diffraction tube, the 50 MΩ. safety resistor can be left in the circuit. This will reduce the maximum shock current to less than 0.1 mA..

Leads used MUST have shrouded connectors and insulation capable of withstanding 5 kV.

Make all connections with the power supply turned off. Do not adjust connections while the EHT is switched on.

Electron beam tubes are fragile. Because they are evacuated, they will implode if they break. The tubes are also expensive, so handle them with great care. Use the purpose-designed holders during practical work.

Note that when switching the EHT supply off, it can take a little while for the voltage output to fall to zero. Allow sufficient time before disconnecting.

Read our standard health & safety guidance


The electron beam strikes a target of a thin deposit of graphitized carbon on a metal grid situated in the exit aperture of the anode. It is the wave nature of electrons passing through the carbon lattice that produces the diffraction pattern.

The cathode is indirectly heated, so it may take a few moments to warm up.

The wavelength, λ, of the electrons is given by De Broglie’s equation λ=h/ p where h is Planck's constant and p is the momentum of an electron.

Procedure

Setting up...

  1. Connect the heater supply of 6.3 volts to the filament.
  2. Connect the filament to the negative terminal of the EHT supply. Earth this terminal.
  3. Connect the positive terminal of the EHT supply to the anode of the diffraction tube. Set the accelerating voltage to about 4,500 volts.
  4. Carrying out...
  5. Switch on the heater supply and the accelerating voltage. Rings should appear on the screen.
  6. Bring a strong magnet close to the tube. Show that the rings are distorted.
  7. Show how the rings change as the voltage is varied between 3,500 and 5,000 volts.

Teaching Notes

  • The diffraction rings are caused by the electrons diffracting and interfering as they pass through the regular crystal structure of the graphite. They are behaving like waves and the graphite’s crystal structure acts as a grating. As the crystals are arranged at any angle, each crystal produces a diffraction pattern, and their diffraction patterns combine around 360° to form rings. This is the same as the microscope slide made from the cut up pieces of a plastic diffraction grating in the

    Two-dimenstional diffraction grating experiment


  • Deflecting the pattern with a magnet shows that the pattern is being produced by moving charged particles, rather than light or some other form of radiation. It introduces the dual nature of the electrons: they behave like particles when they are accelerated, like waves as they pass through the graphite foil, and like particles again as they are deflected in the magnetic field. This is an example of complementarity. See guidance note...

    Electrons behaving like waves


  • The diameter of the rings will change as the accelerating voltage changes. It seems that the more energy the electrons have, the shorter their wavelength.
  • The pattern resulting from the passing of a beam of electrons through graphite is very similar to a beam of X-rays passing through the powdered potassium alum crystal. It suggests that electrons undergo diffraction, and will therefore interfere in the same way as X-rays and other waves.

This experiment was safety-tested in March 2008

Related Guidance

A video showing how to use an electron diffraction tube:

Up next

Electron diffraction tube

Electron
Quantum and Nuclear

Electron diffraction tube

Practical Activity for 14-16

Demonstration

This shows that an electron beam is diffracted when it passes through graphite, suggesting that electrons have a wave-like character.

Apparatus and Materials

  • Electron diffraction tube and stand
  • EHT supply, 0-6 kV variable
  • Connecting wires, including some with shrouded terminals
  • Bar magnet

Health & Safety and Technical Notes

Ensure that the high voltage anode circuit incorporates a protective resistor.

Some EHT supplies have this built-in so that it is in series with the high voltage terminal; others may require you to explicitly wire it in to the circuit.

Using leads with shrouded plugs will ensure that you cannot accidentally come into contact with the high voltage.

Watching the voltmeter which indicates the voltage across the output of the EHT supply will also allow you to judge when the voltage has dropped to a safe level at the end of the demonstration.

Notes on the equipment:

  • The electron diffraction tube is an evacuated glass tube and is therefore fragile and should be handled with care. It is best not to move the tube while the filament is hot. Avoid switching the filament heater on and off unnecessarily.
  • Check that your EHT supply includes a protective high-resistance resistor.
  • It helps to used connecting wires of different colours for the two circuits, e.g. black wires for the filament circuit, red for the high voltage anode circuit and green for the earth connections.

Read our standard health & safety guidance


Procedure

This demonstration shows how a beam of electrons is diffracted as it passes through a graphite film. The film below shows how to set up the diffraction tube so that it can be used safely.

Electron diffraction tube


  1. The demonstration uses a 6 kV supply; teachers may feel that this is daunting and potentially dangerous. However, the film shows that, if you understand the circuits involved, there is no significant danger.
  2. The wiring may seem complex. There are in fact two simple series circuits: a low voltage circuit to the heated filament and a high voltage circuit to provide the accelerating potential between the cathode and the anode.
  3. The diffraction pattern is likely to be faint so you may wish to set the demonstration up in a darkened room, or in a separate darkroom.

Teaching Notes

  • Why do we see a diffraction pattern of rings? This is because the graphite is polycrystalline. The graphite film has regions in which the planes of carbon atoms are in different orientations. The electron beam is quite broad and so it passes through many different regions of the graphite. (If the graphite were a single crystal, a diffraction pattern of discrete spots would be formed.)
  • Why do the rings shrink as the accelerating voltage is increased? The electron beam has a wave character – this is why the beam is diffracted. The wavelength of the beam is shorter than the distance between the atomic planes of the graphite. If the accelerating voltage is increased, the electrons have greater energy and hence shorter wavelength ( E = hc / l ). With a shorter wavelength, the waves are diffracted less and so the diameters of the diffraction rings decrease.
  • Knowing the accelerating voltage and the diameter of a diffraction ring, it would be possible to estimate the atomic spacing in the graphite.
  • Why is the electron beam deflected by a magnetic field? This is an example of the motor effect. The electron beam represents an electric current (in the opposite direction to the beam, since the electron charge is negative). Fleming’s left-hand rule will give the direction of the force on the electrons. You could use Helmholtz coils to produce a uniform and calculable field in the evacuated tube.
  • Once you have mastered this type of electron beam tube, you should feel confident to go on and use others such as the deflection tube and the e / m tube.

Up next

J J Thomson

Electron
Quantum and Nuclear

J J Thomson

Physics Narrative for 14-16

JJ Thomson is intimately connected with the concept of the electron. He is credited with the discovery of electrons. More accurately, he proposed and demonstrated that cathode rays are not massless radiation, but were actually made of small charged particles which he called corpuscles.

Joseph John (J. J.) Thomson was born in England in 1856 and was going to be an engineer. However, after the death of his father (when Thomson was 16), his mother couldn't afford the large apprenticeship fee. So he stayed at college in Manchester and, some years later, won a scholarship to Cambridge University where he worked for the rest of his life.

At the age of 28, Thomson was given the post of Cavendish Professor in the Physics Department at Cambridge University. He was in charge of the laboratory despite, as his assistant put it, "being very awkward with his fingers" and being discouraged from handling the instruments. He was, however, inspired with his designs for apparatus and interpretations of experimental results.

Thomson's work on gas discharges and cathode rays led, in 1897, to his discovery of the electron (his interpretation of the results of deflecting cathode rays).

A theorist as well as an experimenter, Thomson described the plum-pudding model of atomic structure, in which electrons were like negative plums embedded in a pudding of positive matter. This was a first step on the road to the current model of the atom.

Up next

Electron guns

Electron
Quantum and Nuclear

Electron guns

Teaching Guidance for 14-16

When a piece of metal is heated, electrons escape from its surface. These free electrons can be accelerated in a vacuum, producing a beam. The hot metal surface and the accelerating plates are sometimes called an ‘electron gun’.

In an electron gun, the metal plate is heated by a small filament wire connected to a low voltage. Some electrons (the conduction electrons) are free to move in the metal – they are not bound to ions in the lattice. As the lattice is heated, the electrons gain kinetic energy. Some of them gain enough kinetic energy to escape from the metal surface. We sometimes say that they are ‘boiled off’ the surface or ‘evaporate’ from it. Although they do not form a gas in the strictest sense, these are good descriptions.

If the hot metal plate is in a vacuum, then the evaporated electrons are free to move. The electrons can be pulled away from the hot surface of the plate by putting a positive electrode (anode) nearby. The anode is created by connecting an electrode to the positive terminal of a power supply, and the hot plate is connected to its negative terminal. The hot plate is then the cathode.

As soon as the electrons evaporate from the surface of the hot plate, they are pulled towards the anode. They accelerate and crash into the anode. However, if there is a small hole in the anode, some electrons will pass through, forming a beam of electrons that came from the cathode – or a cathode ray.

This cathode ray can be focused and deflected and can carry small currents. This is the basis of the important experiments carried out by J J Thomson and others.

More background on J J Thomson


It is also the basis of early electronic devices.

You could explain the operation of an electron gun thus:

  1. At one end of the tube there is a little rocket shaped gun. In that gun a starting plate is heated by a tiny electric grill. The plate has a special surface that lets electrons loose rather easily. Electrons come off that plate. They are speeded up in the gun by a large potential difference between that starting plate (‘negative cathode’) and the gun muzzle (‘positive anode’)._
  2. Electrons come out at high speed through a tiny hole in the cone-shaped muzzle.
  3. The electrons continue at that constant speed through the vacuum because there is nothing for them to collide with - until they hit a fluorescent screen, where they make a bright spot.
  4. The glass globe of the tube has been pumped out to a very good vacuum, removing air which would soon slow down electrons by collisions. But then a very little helium (or hydrogen) gas is let in. Because the helium atoms give out a green glow when hit by electron, you can see the path of the electrons made visible as a thin line of glow. (Hydrogen glows blue.)
  5. Look at the thin glowing line carefully. You are seeing the path of electrons flying through thin helium (or hydrogen), almost a vacuum, all by themselves, with no wires there.

Focusing

The fine beam tube is improved by adding a small conical electrode – often connected to the anode. This produces a converging electric field which focuses the electrons and produces a tighter beam and sharper spot on the fluorescent screen.

Up next

The speed of electrons

Electron
Quantum and Nuclear

The speed of electrons

Teaching Guidance for 14-16

In an electron gun, electrons are boiled off the surface of a hot metal plate. They leave the plate with very small speeds, and then the electric field accelerates them towards the anode. See the guidance note

Electron guns


You can calculate the electrons' speed by thinking of the energy changes in the system.

Each electron has a charge of e coulombs, and the potential difference between the filament and the anode is V volts.

The energy transferred to each coulomb of charge is V joules.

So the energy transferred to electrons is eV joules.

The electrons gain kinetic energy. Unlike electrons in a wire, these electrons have nothing to hit, nothing to transfer energy to, as they travel towards the anode. So each electron gains kinetic energy equal to the amount of energy transferred electrically.

The electron starts from rest (near enough) so the kinetic energy gained is given by ½mv 2 where m is its mass and v is its speed.

So we can say that: ½mv 2 = eV

The mass of the electron is m = 9 × 10-31 kg

The electronic charge is e = 1.6 × 10-19 C

For an electron gun with a voltage between its cathode and anode of V = 100V the electron will have a speed of about v = 6 × 106 m/s. (Relativistic effects have not been taken into account.)

There will be no more acceleration once the electrons have passed through the anode.

A crude model would be a collection of marbles running down a sloping board to crash into a wall at the bottom, except for a few that might hit a gap in the wall and would continue along on the flat ground on the other side of the wall. The slope corresponds to the electric field we apply inside the gun to accelerate the electrons. The flat ground corresponds to the region beyond the anode where the electrons continue at a constant velocity.

A TV picture tube has just such a gun, to fire electrons straight out to the screen in the tube. There the electrons make a bright spot by exciting a glow on the screen, but on their way they can be pulled out of a straight line by magnetic fields.

Up next

Deflection in electric fields

Electron
Quantum and Nuclear

Deflection in electric fields

Teaching Guidance for 14-16

Most deflection tubes work in a similar way. Electrons are evaporated off a hot cathode (negative). They are accelerated towards an anode (positive) using a high voltage. They emerge from a hole in the anode with a fairly uniform velocity, which remains constant as they cross the tube, which is evacuated. See Guidance note:

Electron guns


With no voltage between the deflecting plates, the electron beam follows the light beam (light produced by the hot filament) in a straight line. With a voltage connected to the plates, the electrons experience a vertical force. The constant vertical force causes the beam to follow a parabolic path. This will be increasingly curved as the deflecting voltage is increased.

Showing the path is parabolic

Once the electrons have passed through the anode there is no accelerating force acting on them so in the horizontal direction the distance travelled, x, is

x = vt (1)

where v is the velocity of the electrons and t is the time for which they are travelling a distance x .

In the vertical direction, the electrons initially have no velocity but experience a force, F .

F = eE

where E is the electric field strength.

They have a mass, m, so this makes them accelerate with an acceleration, a .

a = Fm = eEm

With a uniform acceleration, you can find the vertical distance, y , which the electrons travel by using

y = ½ at 2 = ½  ×  eEm x t 2 (2)

From equations (1) and (2) then

y = eEx 22mv 2 (3)

For a fixed accelerating voltage, v is constant. So everything in the equation is constant apart from x and y. So y varies with the square of x. This is the equation for a parabola.

Taking this a step further, the energy transferred to the electrons is eVa, where Va is the accelerating voltage. As a result of this, the electrons gain kinetic energy, which is given by ½mv 2. So we can say that:

½mv 2 = eVa

v 2 = 2eVam

Substituting in equation (3),

y = Ex 24Va (4)

The electric field strength between the deflecting plates is E = Vdd, where Vd is the deflecting voltage and d is the separation of the plates.

Substituting in equation (4).

y = Vdx 24dVa

Two points to note from this equation:

  1. The deflection is independent of the mass and the charge, so this experiment cannot be used to measure e / m . The reason that it is independent of these values is that, if the charge increases, then the accelerating force increases by the same amount in the electron gun and between the deflection plates. A similar argument applies to any changes of mass.
  2. If Vd and Va are the same (i.e. the accelerating voltage is used for the deflection plates as well), then the shape of the curve is independent of this voltage. It will be a constant shape, which depends only on the separation of the plates.

Up next

Types of electron tube

Electron
Quantum and Nuclear

Types of electron tube

Teaching Guidance for 14-16

There are a number of different cathode ray tubes available to schools. They all use similar electron guns but have different arrangements within the tube. Each one can be used to illustrate or measure slightly different behaviours of electrons. Some of them can be used for a number of different demonstrations. Also, some effects can be demonstrated using more than one tube. Often, your choice of tube will be determined by what you already have available in your school or college.

Here follows a quick overview of each type of tube and what it is best used for.

1 Fine beam tubes

There are two main types of fine beam tube.

a Leybold style tube

These were made in Germany and have a single electron beam. The path of the electrons shows up blue because there is a residual amount of hydrogen gas in the tube. The magnetic field coils are larger than the tube and normally fixed to the base board.

This can be used for basic deflection experiments and e/m measurements. However, a Teltron tube is better adapted for making the beam go in a complete orbit.

b Teltron tube

This second type of tube is made in the UK by the scientific products supplier 3B Scientific (previously manufactured by Teltron). It has two electron beams, so that one beam fires out across the tube and the other one, at right angles to the first beam, up to the top of the tube. The beam is selected using a switch close to the cathode. The paths of the electron beams are green, because the electrons are travelling through a residual amount of helium gas.

Just outside each gun muzzle there is a pair of plates for deflecting the beam by an electric field. One plate of each pair is attached directly to the gun muzzle which supports it. The other plate of each pair is connected inside the tube to the second side terminal on the tube.

These tubes are useful for e/m measurements because, using the vertical gun, it is possible to get the electron beam to go in a closed orbit.

If the beam fails to make a clear spot then try a small potential difference to the deflecting plates. Another trick is to clean the accumulated charges off the screen by sweeping the beam up and down it and across it.

2 Maltese cross tube

The Maltese cross tube is used to show the shadow produced by a piece of metal in the path of an electron beam. The electron gun is similar to other tubes except that the beam is allowed to spread. The metal cross inside the tube casts a shadow on the fluorescent screen.

3 Deflection tube

The beam from the deflection tube is produced by a horizontal slit in the anode. So the beam fans out to produce a ‘V’ of electrons in the horizontal plane. This is aimed at a vertical fluorescent screen inside the tube. The vertical screen is at an angle to the beam direction. So the fan of electrons cuts across the screen, producing a straight line along it.

The deflection plates are positioned above and below the screen, which has its own graduated scale. So the effect of the deflecting voltage can be measured on the scale.

Using the graticule, it is possible to show that the path is parabolic in an electric field and circular in a magnetic field.

The Perrin tube

This tube has a collecting plate and terminal slightly off-axis at the target end of the tube. This is to allow you to deflect the beam and collect electrons. It is possible to show that the collected charge is negative.

Up next

The Millikan experiment

Electron
Quantum and Nuclear

The Millikan experiment

Teaching Guidance for 14-16

The Millikan experiment is hugely important. Between 1910 and 1911 Robert Millikan used some clever ideas and careful experimentation to show that charge is quantized. He then determined a value for the fundamental quantum of charge, known as unit charge.

He could not measure a single quantum of charge. Instead, he measured the charge on a number of oil drops and deduced that they could all be divided by a single factor, which must be the basic unit of charge.

The Millikan experiment is very fiddly and difficult to perform in school. It is more likely that you will use a film clip or simulation of the experiment to show its principles to students. The principles are:

  • An oil drop will fall through air under its own weight. If the drop is given a charge, it can be suspended using an electric field. At this point the electrostatic force balances the weight of the drop. The size of the electrostatic force depends on the charge on the drop. So Millikan could work out the charge as long as he knew the weight.
  • In order to find the weight of the drop, Millikan allowed the drop to fall through air. It quickly reaches its terminal velocity. At this point, the weight is being balanced by the viscous drag of the air. The drag can be calculated from Stokes' Law which allowed Millikan to determine the weight.
  • Millikan repeated the experiment for over 150 oil drops. He selected 58 of his results and found the highest common factor. That is, the single unit of charge which could be multiplied up to give the charge he measured on all his oil drops.

The calculations

1 When the oil drop is in the electric field, there is an electric force, F , acting upwards. This is given by:

F = Eq where q is the charge on the oil drop and E is the field strength.

= Vqd where V is the voltage on the plates and d is their separation.

The drop is being pulled down by its weight, mg. When the drop is suspended and stationary, the net force is zero. So:

  • Vqdmg = 0
  • Vqd = mg
  • so q = mgdV

2 To find the weight of the drop, Millikan let it fall through the air and measured its terminal velocity. At this point, the net force is zero – i.e. weight is balanced by the viscous drag. The viscous drag, D , is given by:

D = 6πη vr where η is the viscosity of air, r is the radius of a spherical drop and v is its speed.

This allowed him to work out the radius of the drop and therefore its weight.

[An experimental alternative is to use the electric field to change the terminal velocity of the oil drop rather than keep it stationary. This is easier to achieve and measure experimentally. It is then possible to derive an expression for the charge which is related to the two velocities. However, for school students, the principle of the stationary drop is probably easier to grasp.]

3 Having measured the charge on a number of oil drops, q1, q2, q3, etc, Millikan reasoned that each charge must be a whole number multiple of the fundamental charge, e. So:

q1 ,=n1 e , q2 ,=n2 e , q3 ,=n3 e and so on, where n is a whole number in each case.

So he found e by finding the highest common factor of all the values of charge that he measured on the oil drops.

Up next

The Millikan story – a tale of mixed results

Electron
Quantum and Nuclear

The Millikan story – a tale of mixed results

Teaching Guidance for 14-16

Millikan recorded the results for 175 drops. He used 58 of those to calculate a value for the charge on an electron, e , which he found as 1.592 x 10 -19 coulombs. The accepted value is now 1.602 x 10 -19 C. He won the Nobel Prize in 1923, partly for this work.

In the 1970s, there were some questions raised over Millikan's selective use of data, most famously by Gerald Holton in Subelectrons, Presuppositions and the Millikan-Ehrenhaft Dispute. Holton referred back to Millikan's original laboratory notes and compared them to his published paper. Millikan had rejected over two thirds of his results. His laboratory notes contain comments such as "This is almost exactly right and the best one I ever had!!!", "Error high will not use" and "Too high by 1.5%".

The debate, known as the Millikan-Ehrenhaft dispute has continued amongst historians and philosophers of science since then. The harshest view is that he massaged or fiddled his results. However, many people now accept that he discarded some results for sound experimental reasons – for example, many of his early results were left out; presumably he thought that his technique was improving as time went on. Also, it can be argued that he omitted obvious outliers.

However, the question remains why he did not own up to this. In his published paper he claimed that "this is not a selected group of drops but represents all of the drops experimented on during 60 consecutive days...". Presumably, he was keen to keep his margin of uncertainty as low as possible (quoted as 0.02 x 10 -19 C).

Furthermore, even before Holton, Richard Feynman had referred to the shame felt by physicists who came after Millikan saying that they had ignored perfectly good results for the measurement of e if they did not match Millikan's closely enough. He said that "We have learned a lot from experience about how to handle some of the ways we fool ourselves."

Many aspects of this story would form the basis of an interesting discussion about how science works. A quick search on the internet for "Millikan-Ehrenhaft Dispute" will yield many interesting links.

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