22. An electron is accelerated from rest through a potential difference V. What is the maximum speed

An electron is accelerated from rest through a potential difference V. What is the maximum speed of the electron?
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In this video, we explore an MCQ from IBDP Paper-1, TZ2 Physics SL, May 2023 Exam. This question tests your understanding of electric potential and its role in accelerating charged particles. Specifically, it asks for the maximum speed of an electron that starts from rest when accelerated through a given potential difference V.
About the Problem
This question requires you to connect key concepts from electrostatics and kinetic energy. As the electron moves through the potential difference, the electrical energy it gains converts into kinetic energy. The crux of solving this problem lies in recognizing that the energy provided by the potential difference is equal to the kinetic energy acquired by the electron.
To solve it, you need:
1. Charge of the electron (e)
2. Mass of the electron (m)
3. Potential difference (V)
Key Concepts Related to the Solution
• Electric Potential Energy and Kinetic Energy: The work done by the electric field to move the electron through a potential difference V translates entirely into the electron's kinetic energy, assuming no other forces act.
• Conservation of Energy: This problem highlights the conversion between potential energy and kinetic energy, emphasizing the principle of energy conservation in physics.
• Charge-to-Mass Ratio: The relationship between the electron’s charge and its mass plays a crucial role in determining how fast it can move under the influence of an electric field.
When working through the problem, students need to focus on inputting the correct values for the charge of the electron (1.6 × 10⁻¹⁹ C) and mass of the electron (9.1 × 10⁻³¹ kg). The potential difference V will be given in the question, and substituting all these values into the kinetic energy equation will yield the correct speed.
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Learner Profiles & Skills Developed
This question aligns with the IB Learner Profile traits of Thinkers and Inquirers. It challenges students to apply analytical reasoning and problem-solving skills to connect concepts across multiple areas of physics. Students also develop a deeper understanding of conceptual reasoning and energy transformations, which are essential skills for success in physics.
The problem encourages the following skills:
1. Analytical Thinking: Breaking down the connection between potential difference and kinetic energy.
2. Problem Solving: Identifying key parameters like charge and mass and using them correctly.
3. Time Management: Managing time efficiently, especially in a timed exam setting.
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Difficulty Level
This problem is moderately difficult. While the underlying concept is straightforward, many students may struggle with correctly identifying the input values and applying them accurately. Additionally, the problem is designed to test not just rote memorization but conceptual understanding of electric fields, energy conservation, and charge dynamics.
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How to Use This Video Effectively
Before you watch the solution, pause the video and try solving the question on your own. Focus on the key concepts mentioned earlier and ensure you input the correct charge and mass values. If you find it challenging or don’t arrive at the correct answer, continue watching the video to understand the approach.
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Enquiry Questions for Further Exploration
Here are some questions to deepen your understanding of the topic:
1. What would happen to the speed of the electron if the potential difference were doubled?
2. How would the answer change if the charged particle were a proton instead of an electron?
3. What other real-world applications can you think of where electric fields are used to accelerate particles?
4. How does the mass of a particle affect its speed under the same potential difference?
5. In what scenarios would the electron not reach the maximum speed predicted by this equation?
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This video is part of our efforts to make IBDP Physics concepts more accessible. Make sure to subscribe for more solutions to past paper questions, and don’t forget to share it with your peers!
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