Table 1 shows results of an experiment to investigate how the de Broglie wavelength $ar{\lambda}$ of an electron varies with its velocity $v$. | $v / 10^7 \, \text{ms}^{-1}$ | $\bar{\lambda} / 10^{-11} \text{m}$ | |-------------------------------|-----------------------------| | 1.5 | 4.9 | | 2.5 | 2.9 | | 3.5 | 2.1 | Show that the data in Table 1 are consistent with the relationship $\bar{\lambda} \propto \frac{1}{v}$. 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.

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Table 1 shows results of an experiment to investigate how the de Broglie wavelength $ar{\lambda}$ of an electron varies with its velocity $v$ - AQA - A-Level Physics - Question 2 - 2018 - Paper 1

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Table 1 shows results of an experiment to investigate how the de Broglie wavelength $ar{\lambda}$ of an electron varies with its velocity $v$. | $v / 10^7 \, \text... show full transcript

Worked Solution & Example Answer:Table 1 shows results of an experiment to investigate how the de Broglie wavelength $ar{\lambda}$ of an electron varies with its velocity $v$ - AQA - A-Level Physics - Question 2 - 2018 - Paper 1

Step 1

Show that the data in Table 1 are consistent with the relationship $\bar{\lambda} \propto \frac{1}{v}$

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Answer

To analyze how the de Broglie wavelength $\bar{\lambda}$ varies with velocity $v$ , we start with the de Broglie equation:

$\bar{\lambda} = \frac{h}{mv}$

Where:

$h$ is Planck's constant
$m$ is the mass of the electron

From the table:

For $v = 1.5 \times 10^7 \, \text{ms}^{-1}, \bar{\lambda} = 4.9 \times 10^{-11} \text{m}$
For $v = 2.5 \times 10^7 \, \text{ms}^{-1}, \bar{\lambda} = 2.9 \times 10^{-11} \text{m}$
For $v = 3.5 \times 10^7 \, \text{ms}^{-1}, \bar{\lambda} = 2.1 \times 10^{-11} \text{m}$

Calculating the ratio of values:

The ratios of $\bar{\lambda}$ to $v$ indicate a relationship where $\bar{\lambda}$ decreases as $v$ increases, affirming $\bar{\lambda} \propto \frac{1}{v}$ .

Step 2

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

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Answer

Using two sets of data from Table 1 to estimate Planck's constant:

For $v = 1.5 \times 10^7 \, \text{ms}^{-1}$ and $\bar{\lambda} = 4.9 \times 10^{-11} \text{m}$ :
- Substituting into de Broglie equation: $h = \bar{\lambda} \cdot mv \implies h = (4.9 \times 10^{-11} m)(9.11 \times 10^{-31} kg)(1.5 \times 10^{7} \text{ms}^{-1}).$
- This gives a calculated value for $h$ .
For $v = 3.5 \times 10^7 \, \text{ms}^{-1}$ and $\bar{\lambda} = 2.1 \times 10^{-11} \text{m}$ :
- Similarly: $h = (2.1 \times 10^{-11} m)(9.11 \times 10^{-31} kg)(3.5 \times 10^{7} \text{ms}^{-1}).$
- This will provide another calculated value for $h$ .

By averaging the two values obtained for $h$ , an appropriate estimate can be determined.

Step 3

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.

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Answer

The interference pattern observed on the screen indicates that the electrons exhibit wave-like behavior. This is characterized by:

Fringe Patterns: The alternating light and dark bands on the fluorescent screen suggest constructive and destructive interference, typical of waves interacting rather than particles traveling independently.
Diffraction Effects: Waves spread out after passing through the graphite, consistent with wave motion, reinforcing the notion that the electron beam can be treated as a wave.

These observations collectively imply that the electrons are demonstrating wave properties, evidenced by the produced interference pattern.

Step 4

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

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Answer

The emission of light from the fluorescent screen when electrons strike it indicates particle-like behavior because:

Localized Interaction: When electrons collide with the screen material, they deposit their energy, producing light. This is characteristic of particle interactions where energy is transferred upon impact.
Discrete Emission Events: The light emitted is often bright, suggesting that each electron impact emits a photon, supporting the concept of electrons behaving like discrete particles.

Thus, the particle nature of electrons is demonstrated by the localized energy transfer resulting in visible light emission.

Table 1 shows results of an experiment to investigate how the de Broglie wavelength $ar{\lambda}$ of an electron varies with its velocity $v$ - AQA - A-Level Physics - Question 2 - 2018 - Paper 1

Worked Solution & Example Answer:Table 1 shows results of an experiment to investigate how the de Broglie wavelength $ar{\lambda}$ of an electron varies with its velocity $v$ - AQA - A-Level Physics - Question 2 - 2018 - Paper 1

Show that the data in Table 1 are consistent with the relationship $\bar{\lambda} \propto \frac{1}{v}$

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

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.

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Table 1 shows results of an experiment to investigate how the de Broglie wavelength $ar{\lambda}$ of an electron varies with its velocity $v$ - AQA - A-Level Physics - Question 2 - 2018 - Paper 1

Worked Solution & Example Answer:Table 1 shows results of an experiment to investigate how the de Broglie wavelength $ar{\lambda}$ of an electron varies with its velocity $v$ - AQA - A-Level Physics - Question 2 - 2018 - Paper 1