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Figure 3 shows part of the apparatus used to investigate electron diffraction - AQA - A-Level Physics - Question 3 - 2019 - Paper 7

Question 3

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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 th... show full transcript

Worked Solution & Example Answer:Figure 3 shows part of the apparatus used to investigate electron diffraction - AQA - A-Level Physics - Question 3 - 2019 - Paper 7

Step 1

State de Broglie's hypothesis.

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Answer

De Broglie’s hypothesis states that all matter particles exhibit wave-like properties, which means that they have a wavelength associated with their momentum. Mathematically, this is expressed as:

ext{wavelength} (\\lambda) = \frac{h}{p}

where $h$ is Planck's constant and $p$ is the momentum of the particle.

Step 2

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

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Answer

The kinetic energy (KE) of the electrons can be calculated using the formula:

KE = eV

where $e$ is the charge of the electron ( $1.6 imes 10^{-19} ext{ C}$ ) and $V$ is the voltage (3.5 kV or $3.5 imes 10^{3} ext{ V}$ ).

Thus,

KE = (1.6 imes 10^{-19}) imes (3.5 imes 10^{3}) \approx 5.6 imes 10^{-16} ext{ J}

Next, we can find the momentum $p$ using:

p = \sqrt{2m_e KE}

where $m_e$ is the electron mass ( $9.11 imes 10^{-31} ext{ kg}$ ).

Substituting the values,

p = \sqrt{2 \times (9.11 imes 10^{-31}) \times (5.6 \times 10^{-16})} \approx 1.43 \times 10^{-24} ext{ kg m/s}

Then, using de Broglie's relation, the wavelength can be calculated as:

\lambda = \frac{h}{p} = \frac{6.626 \times 10^{-34}}{1.43 \times 10^{-24}} \approx 4.63 \times 10^{-10} ext{ m} = 0.463 ext{ nm}

This is not consistent with a wavelength of 0.02 nm.

Step 3

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.

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Answer

Use target with greater spacing between atoms. This change would allow for a wider range of diffraction angles, leading to a distinct pattern.
Increase the incident energy (voltage). Raising the voltage would increase the electron energy and, consequently, its momentum, allowing for a finer diffraction pattern which results in clearer rings in the interference pattern.

Figure 3 shows part of the apparatus used to investigate electron diffraction - AQA - A-Level Physics - Question 3 - 2019 - Paper 7

Worked Solution & Example Answer:Figure 3 shows part of the apparatus used to investigate electron diffraction - AQA - A-Level Physics - Question 3 - 2019 - Paper 7

State de Broglie's hypothesis.

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

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.

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