Thermionic emission

This question is about Thomson’s determination of the electron’s specific charge.

You should not use the values of the electron charge, mass or specific charge from the data and formulae booklet in this question.

Figure 1 shows part of the apparatus that Thomson used to measure the specific charge of the electron.

A modern version of Thomson’s apparatus uses thermionic emission in the production of the electron beam.

Suggest how the electron beam is produced in this modern version. You should include a labelled diagram and suitable values for the power supplies used.

A potential difference (pd) of 750 V is applied between the horizontal parallel plates. Figure 2 shows the plates and the path of the electrons.

The electrons enter the electric field between the plates at S and leave it at T with speed v. Beyond T the electrons travel in a straight line at an angle θ. θ is read from a scale on a fluorescent screen.

The plates are of length 10.0 cm and are separated by a distance of 5.00 cm.

A uniform magnetic field of flux density 0.640 mT is now applied between the plates. This returns the electron beam to its undeflected position.

Show that the horizontal component of the velocity of the electrons is approximately

The magnetic field is switched off and θ is measured to be 25°.

Show that the vertical component of the velocity of the electrons at T is approximately

Show that the vertical acceleration of the electrons between the plates is

Determine a value for the specific charge of the electron.

Explain the significance of the result of Thomson’s determination.

Some students are given a version of the apparatus to repeat Thomson’s experiment.

Figure 3 shows a section of the measuring scale on the fluorescent screen and the spot from the electron beam.

The students consider two methods for minimising the percentage uncertainty in the measurement of the angle.

Method 1:

• choose a magnetic flux density B

• then set the magnetic flux density to B with no pd

• then adjust only the pd until the beam is horizontal

• then switch off the magnetic field and measure the angle θ.

Method 2:

• choose an angle θ

• then set the pd so that the spot from the electron beam is at θ with no magnetic field

• then adjust only the magnetic field until the beam is horizontal.

Discuss both of these methods with reference to the percentage uncertainty in θ that they will produce. In your answer, suggest which method will minimise the percentage uncertainty. No calculations are required.

Figure 3 shows a modern version of Bertozzi’s experiment to measure the kinetic energy of high-speed electrons. A timer is used to measure the time taken for a pulse of electrons to travel from the detector to the aluminium block.

A potential difference (pd) of 1.30 MV is used to accelerate the electrons.

Show that each electron gains approximately 2 × 10⁻¹³ J of kinetic energy.

These electrons cause the temperature of the aluminium block to increase by 68.0 K The number of electrons that cause this increase in temperature is 4.50 × 10¹⁷

Deduce whether this increase in temperature is consistent with an accelerating pd of 1.30 MV.

specific heat capacity of aluminium = 903 J kg⁻¹ K⁻¹ mass of aluminium block = 1.50 kg

The speed of the electrons between the detector and the block is 2.88 × 10⁸ m s⁻¹.

Student A suggests that the non-relativistic equation for kinetic energy could be used. Student B suggests that the relativistic equation for kinetic energy is required in this situation.

Evaluate the suggestions of student A and student B. Support your answer with calculations.

The timer in Figure 3 records a time of 29.8 ns.

What is the proper time interval for an electron travelling from the detector to the aluminium block?

Tick (✓) one box.

The electrons in Figure 3 were accelerated from rest in 13 stages.

In each stage the electrons were accelerated by a pd of 100 kV.

As a result, an electron increases its speed and kinetic energy during each stage.

Compare, for an electron,

• its increase in speed for the first stage with that for the last stage

• its increase in kinetic energy for the first stage with that for the last stage.

Justify your answer.

No further calculations are required.

In Figure 1, a beam of electrons travels through the aperture in the anode and hits the screen.

Explain how the electrons that form the beam are emitted.

Show that the maximum speed of the electrons in the beam is about 1.3 × 10⁷ m s⁻¹.

A student suggests that the apparatus can be used to demonstrate the wave properties of electrons in the beam, provided that the aperture in the anode has a suitable diameter.

Discuss whether the student is correct. Support your answer with a calculation.

In 1897, J J Thomson determined a value for the specific charge of an unknown particle. The unknown particle is now known to be the electron.

Describe one method to determine the specific charge of the electron.

Your answer should include:

• a description of the apparatus used and the measurements made

• a description of how the specific charge can be determined using these measurements

• an explanation of the conclusion made by Thomson from the value that he determined.

Figure 1 shows the apparatus used in an experiment to investigate electron diffraction and the de Broglie hypothesis.

Explain how high-speed electrons are produced in the apparatus in Figure 1.

In your answer you should:

• name parts A and B

• discuss the purposes of potential differences V₁ and V₂.

In the experiment, electrons are incident on a target made of a crystalline material. The electron wavelengths need to be about 50% the size of an atom to produce a diffraction pattern on the screen.

Suggest a suitable value for V₂. Support your answer with a calculation.

Figure 2 shows a typical diffraction pattern produced on the screen by the electrons.

Explain how measurements made with the apparatus in Figure 1 can be used to support the de Broglie hypothesis.

STM and TEM are abbreviations for two types of electron microscope.

Which row links the type of microscope to a relevant property of moving electrons?

Figure 3 shows part of the apparatus used to investigate electron diffraction.

Electrons were accelerated through a potential difference to form a beam which was then incident on a thin metal foil.

Regions of maximum and minimum intensity formed on a photographic film behind the

State de Broglie’s hypothesis.

The voltmeter in Figure 3 shows a reading of 3.5 kV.

Determine whether this voltmeter reading is consistent with a de Broglie wavelength for the electrons in the beam of about 0.02 nm.

The experiment is repeated using a similar arrangement to that shown in Figure 3. Figure 4 shows the diffraction patterns from the two experiments.

State and explain two independent changes that could be made to the arrangement in Figure 3 to produce the result shown for the second experiment in Figure 4.

Figure 1 shows apparatus which can be used to determine the specific charge of an electron.

Electrons are emitted from the filament and accelerated by a potential difference between the filament and anode to produce a beam. The beam is deflected into a circular path by applying a magnetic field perpendicular to the plane of the diagram.

Describe the process that releases the electrons emitted at the filament.

Table 1 shows the data collected when determining the specific charge of the electron by the method shown in Figure 1.

Show that the specific charge of the electron is given by the expression

Using data from Table 1, calculate a value for the specific charge of the electron. Give your answer to an appropriate number of significant figures.

At the time when Thomson measured the specific charge of the particles in cathode rays, the largest specific charge known was that of the hydrogen ion.

State how Thomson’s result for the specific charge of each particle within a cathode ray compared with that for the hydrogen ion and explain what he concluded about the nature of the particles.

What is the process by which electrons are produced in an electron gun? Tick () the correct box.

The electrons in a particular TEM have a kinetic energy of 4.1 × 10^–16 J. Relativistic effects are negligible for this electron energy.

Suggest, with a calculation, whether the images of individual atoms can, in principle, be resolved in this TEM.

A typical TEM can accelerate electrons to very high speeds and form high resolution images.

Explain:

the process of image formation, and

the factors that affect the quality of, and the level of detail in, the image.