Worksheet: The Heisenberg Uncertainty Principle

In this worksheet, we will practice calculating the minimum uncertainty in the momentum of a particle given the minimum uncertainty in its position, and vice versa.

Q1:

The minimum uncertainty in the wavenumber of a photon is 54,000 māˆ’1. Use the formula Ī”š‘„Ī”š‘˜ā‰„12 to find the minimum uncertainty in the position of the photon. Give your answer to 3 significant figures.

  • A4.63Ɨ10ļŠ±ļŠ¬ m
  • B9.26Ɨ10ļŠ±ļŠ¬ m
  • C7.41Ɨ10ļŠ±ļŠ« m
  • D3.70Ɨ10ļŠ±ļŠ« m
  • E1.84Ɨ10ļŠ±ļŠ« m

Q2:

Fill in the blanks: As the uncertainty in the momentum of a particle , the uncertainty in the position of the particle .

  • AIncreases, increases
  • BDecreases, increases
  • CDecreases, decreases

Q3:

The minimum uncertainty in the position of a photon is 12 nm. Use the formula Ī”š‘„Ī”š‘˜ā‰„12 to find the minimum uncertainty in the wavenumber of the photon. Give your answer to 3 significant figures.

  • A3.33Ɨ10ļŠ® māˆ’1
  • B4.17Ɨ10ļŠ­ māˆ’1
  • C1.67Ɨ10ļŠ® māˆ’1
  • D2.08Ɨ10ļŠ­ māˆ’1
  • E8.33Ɨ10ļŠ­ māˆ’1

Q4:

Fill in the blank: As the uncertainty in the position of a particle , the uncertainty in its momentum .

  • Adecreases, increases
  • Bincreases, increases
  • Cdecreases, decreases

Q5:

An electron in a particle accelerator has an uncertainty in its position of 5.11Ɨ10ļŠ±ļŠ§ļŠŖ m. Using the formula Ī”š‘„Ī”š‘ā‰„ā„Ž4šœ‹, calculate the minimum possible uncertainty in the momentum of the electron. Use a value of 6.63Ɨ10ā‹…ļŠ±ļŠ©ļŠŖJs for the Planck constant. Give your answer to 3 significant figures.

  • A4.13Ɨ10ļŠ±ļŠØļŠ§ kgā‹…m/s
  • B3.24Ɨ10ļŠ±ļŠØļŠ§ kgā‹…m/s
  • C1.03Ɨ10ļŠ±ļŠØļŠ§ kgā‹…m/s
  • D5.11Ɨ10ļŠ±ļŠ§ļŠŖ kgā‹…m/s
  • E2.06Ɨ10ļŠ±ļŠØļŠ§ kgā‹…m/s

Q6:

A high-energy photon scatters off an electron in a target. Before the collision, the uncertainty in the momentum of the photon is 8.29Ɨ10ļŠ±ļŠØļŠ¬ kgā‹…m/s. Using the formula Ī”š‘„Ī”š‘ā‰„ā„Ž4šœ‹, calculate the minimum possible uncertainty in the position of the photon. Use a value of 6.63Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s for the Planck constant. Give your answer to 3 significant figures.

Q7:

Five curves are shown on the graph. Which curve shows how the minimum uncertainty in the momentum of a particle varies with the minimum uncertainty in its position?

  • AThe red line
  • BThe black line
  • CThe blue line
  • DThe green line
  • EThe violet line

Q8:

A proton moving through free space has an uncertainty in its momentum of 4.00Ɨ10ļŠ±ļŠØļŠ® kgā‹…m/s. Using the formula Ī”š‘„Ī”š‘ā‰„ā„Ž4šœ‹, calculate the minimum possible uncertainty in the position of the proton. Use a value of 6.63Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s for the Planck constant. Give your answer to 3 significant figures.

Q9:

Which of the following formulas correctly shows how the minimum uncertainty in the position of a particle varies with the minimum uncertainty in its momentum?

  • AĪ”š‘„āˆĪ”š‘
  • BĪ”š‘„āˆĪ”š‘2
  • CĪ”š‘„āˆĪ”š‘ļŠØ
  • DĪ”š‘„āˆ1Ī”š‘ļŠØ
  • EĪ”š‘„āˆ1Ī”š‘

Q10:

A muon that is produced in a particle accelerator has an uncertainty in its position of 2.00Ɨ10ļŠ±ļŠ§ļŠ§ m. Using the formula Ī”š‘„Ī”š‘ā‰„ā„Ž4šœ‹, calculate the minimum possible uncertainty in the momentum of the muon. Use a value of 6.63Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s for the Planck constant. Give your answer to 3 significant figures.

  • A2.00Ɨ10ļŠ±ļŠ§ļŠ§ kgā‹…m/s
  • B6.63Ɨ10ļŠ±ļŠ©ļŠŖ kgā‹…m/s
  • C5.28Ɨ10ļŠ±ļŠØļŠŖ kgā‹…m/s
  • D8.29Ɨ10ļŠ±ļŠØļŠŖ kgā‹…m/s
  • E2.64Ɨ10ļŠ±ļŠØļŠŖ kgā‹…m/s

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