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If an electron's position can be measured to a precision of 3.0 × 10¬8 m, how precisely can its speed be known?

If an electron's position can be measured to a precision of 3.0 × 10¬8 m, how precisely can its speed be known?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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I listed all of the answers that are incorrect. Please help!

### Quantum Mechanics Problem: Precision in Measuring an Electron's Speed **Problem Statement:** If an electron's position can be measured to a precision of \(3.0 \times 10^{-8}\) m, how precisely can its speed be known? **Instructions:** Express your answer to two significant figures and include the appropriate units. **Answer Submission:** - Input: \(\Delta v = 1.9 \times 10^3 \, \text{m/s}\) **Feedback on Submitted Answers:** 1. **Answer 1:** - \(\Delta v = 2 \times 10^3 \, \text{m/s}\) - Deduction: -3% 2. **Answer 2:** - \(\Delta v = 1.92 \times 10^3 \, \text{m/s}\) - Deduction: -3% 3. **Answer 3:** - \(\Delta v = 1.8 \times 10^3 \, \text{m/s}\) - Deduction: -3% 4. **Answer 4:** - \(\Delta v = 1.9 \times 10^3 \, \text{m/s}\) - Deduction: -3% **Explanation:** - This problem involves calculating the uncertainty in the speed of an electron when its position is known to a certain precision. - The correct expression acknowledges the need to provide the answer with two significant figures and proper units of measurement. **Note:** All submitted answers receive a deduction of -3% suggesting that none of the responses are completely accurate according to the criteria set by the problem (e.g., such as round-off errors, or adherence to significant figures and unit conventions). Further review or guidance on these common pitfalls may be necessary.
Transcribed Image Text:### Quantum Mechanics Problem: Precision in Measuring an Electron's Speed **Problem Statement:** If an electron's position can be measured to a precision of \(3.0 \times 10^{-8}\) m, how precisely can its speed be known? **Instructions:** Express your answer to two significant figures and include the appropriate units. **Answer Submission:** - Input: \(\Delta v = 1.9 \times 10^3 \, \text{m/s}\) **Feedback on Submitted Answers:** 1. **Answer 1:** - \(\Delta v = 2 \times 10^3 \, \text{m/s}\) - Deduction: -3% 2. **Answer 2:** - \(\Delta v = 1.92 \times 10^3 \, \text{m/s}\) - Deduction: -3% 3. **Answer 3:** - \(\Delta v = 1.8 \times 10^3 \, \text{m/s}\) - Deduction: -3% 4. **Answer 4:** - \(\Delta v = 1.9 \times 10^3 \, \text{m/s}\) - Deduction: -3% **Explanation:** - This problem involves calculating the uncertainty in the speed of an electron when its position is known to a certain precision. - The correct expression acknowledges the need to provide the answer with two significant figures and proper units of measurement. **Note:** All submitted answers receive a deduction of -3% suggesting that none of the responses are completely accurate according to the criteria set by the problem (e.g., such as round-off errors, or adherence to significant figures and unit conventions). Further review or guidance on these common pitfalls may be necessary.
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