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 $V_1$ and $V_2$. [4 marks] 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 $V_2$. $V_2 = $ ______ V [4 marks] 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. [4 marks] 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? Tick (✓) one box.

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Figure 1 shows the apparatus used in an experiment to investigate electron diffraction and the de Broglie hypothesis - AQA - A-Level Physics - Question 1 - 2021 - Paper 7

Question 1

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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 ... show full transcript

Worked Solution & Example Answer:Figure 1 shows the apparatus used in an experiment to investigate electron diffraction and the de Broglie hypothesis - AQA - A-Level Physics - Question 1 - 2021 - Paper 7

Step 1

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

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Answer

Parts A and B of the apparatus serve specific functions in producing high-speed electrons:

Part A: This is the filament, which acts as a heated cathode. When a voltage is applied, it gets heated and emits electrons through thermionic emission.
Part B: This is the anode. It is positively charged and attracts the emitted electrons, allowing them to accelerate towards it due to the electric field created by the potential difference $V_1$ .

The potential difference $V_1$ supplies energy to drive the current and, therefore, heats the cathode, which is crucial for creating the electron beam. The potential difference $V_2$ is responsible for producing the electric field necessary to accelerate the electrons towards the target.

Step 2

Suggest a suitable value for $V_2$.

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Answer

Given the criteria that electron wavelengths need to be about 50% the size of an atom (approximately $0.1 ext{ nm}$ or $1 imes 10^{-10} ext{ m}$ ), we can calculate the required wavelength using the de Broglie relation:

$ext{wavelength} = rac{h}{p}$

where $h$ is the Planck constant and $p$ is the momentum of the electrons. Assuming a suitable kinetic energy obtained from the potential difference $V_2$ matches this requirement, a calculated value for $V_2$ is approximately $0.5 ext{ V}$ to provide the necessary energy to achieve the desired electron wavelength.

Step 3

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

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Answer

The apparatus allows for direct observations of electron diffraction patterns, which provide evidence for wave behavior of electrons. According to the de Broglie hypothesis, particles such as electrons exhibit wave-like characteristics with a wavelength given by

$ext{wavelength} = rac{h}{p}$

where $p$ is the momentum of the electron. By measuring the angles and spacing of the diffraction rings produced on the screen in Figure 2, researchers can correlate these measurements with calculated wavelengths from the energy of the electrons, thus supporting the theory that electrons can behave as waves, consistent with the de Broglie hypothesis.

Step 4

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

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Answer

For this question, the appropriate answer is:

STM	TEM
Moving electrons can cross a potential barrier.	Moving electrons can be deflected by a magnetic field.

Figure 1 shows the apparatus used in an experiment to investigate electron diffraction and the de Broglie hypothesis - AQA - A-Level Physics - Question 1 - 2021 - Paper 7

Worked Solution & Example Answer:Figure 1 shows the apparatus used in an experiment to investigate electron diffraction and the de Broglie hypothesis - AQA - A-Level Physics - Question 1 - 2021 - Paper 7

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

Suggest a suitable value for $V_2$.

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

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

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