Wave-particle duality

Which row provides evidence for the particle nature of light and the wave nature of light?

An alpha particle has a speed of 4.5 × 10⁵ m s⁻¹.

What is the de Broglie wavelength of the alpha particle?

An electron and a proton move with the same speed.

What is de Broglie wavelength of electron ? de Broglie wavelength of proton

Electrons with a certain kinetic energy pass through a powdered crystalline sample and are incident on a fluorescent screen. The diagram shows a sketch of the diffraction pattern produced.

A change is made and this second pattern is produced.

Which change could produce the second pattern?

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.

Which row gives evidence for the wave nature of electrons and evidence for the particulate

Which particle has the smallest de Broglie wavelength?

A muon and an electron are travelling at the same speed.

Which row gives the particle with the greater kinetic energy and the particle with the longer de Broglie wavelength?

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?

Which graph shows the variation of momentum p with wavelength λ of a photon?

The scanning tunnelling microscope (STM) uses a process called quantum tunnelling.

Explain what is meant by quantum tunnelling of an electron in an STM. You may include a diagram as part of your answer.

An STM is used to map the positions of the atoms between points A and B on the surface of a sample.

Figure 3 shows some of the features of the operation of an STM.

The STM in Figure 3 is in constant-current mode.

Describe how the STM creates a map of the positions of one row of atoms on the surface of the sample from A to B.

The smallest size of objects that the STM can resolve is similar to the de Broglie wavelength of the tunnelling electrons.

Deduce whether electrons with kinetic energies less than 1.5 eV are suitable to map the surface in Figure 3.

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.

Table 1 shows results of an experiment to investigate how the de Broglie

Calculate a value for the Planck constant suggested by the data in Table 1.

Figure 2 shows the side view of an electron diffraction tube used to demonstrate the wave properties of an electron.

An electron beam is incident on a thin graphite target that behaves like the slits in a diffraction grating experiment. After passing through the graphite target the electrons strike a fluorescent screen.

Figure 3 shows the appearance of the fluorescent screen when the electrons are incident on it.

Explain how the pattern produced on the screen supports the idea that the electron beam is behaving as a wave rather than as a stream of particles.

Explain how the emission of light from the fluorescent screen shows that the electrons incident on it are behaving as particles.

What is the speed of the electrons?

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.