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‰„ 1 2 to find the minimum uncertainty in the position of the photon. Give your answer to 3 significant figures.

  • A 3 . 7 0 Ɨ 1 0 ļŠ± ļŠ« m
  • B 4 . 6 3 Ɨ 1 0 ļŠ± ļŠ¬ m
  • C 9 . 2 6 Ɨ 1 0 ļŠ± ļŠ¬ m
  • D 1 . 8 4 Ɨ 1 0 ļŠ± ļŠ« m
  • E 7 . 4 1 Ɨ 1 0 ļŠ± ļŠ« m

Q2:

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

  • ADecreases, decreases
  • BIncreases, increases
  • CDecreases, increases

Q3:

The minimum uncertainty in the position of a photon is 12 nm. Use the formula Ī” š‘„ Ī” š‘˜ ā‰„ 1 2 to find the minimum uncertainty in the wavenumber of the photon. Give your answer to 3 significant figures.

  • A 4 . 1 7 Ɨ 1 0 ļŠ­ māˆ’1
  • B 8 . 3 3 Ɨ 1 0 ļŠ­ māˆ’1
  • C 1 . 6 7 Ɨ 1 0 ļŠ® māˆ’1
  • D 2 . 0 8 Ɨ 1 0 ļŠ­ māˆ’1
  • E 3 . 3 3 Ɨ 1 0 ļŠ® māˆ’1

Q4:

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

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

Q5:

An electron in a particle accelerator has an uncertainty in its position of 5 . 1 1 Ɨ 1 0 ļŠ± ļŠ§ ļŠŖ m. Using the formula Ī” š‘„ Ī” š‘ ā‰„ ā„Ž 4 šœ‹ , calculate the minimum possible uncertainty in the momentum of the electron. Use a value of 6 . 6 3 Ɨ 1 0 ā‹… ļŠ± ļŠ© ļŠŖ J s for the Planck constant. Give your answer to 3 significant figures.

  • A 4 . 1 3 Ɨ 1 0 ļŠ± ļŠØ ļŠ§ kgā‹…m/s
  • B 1 . 0 3 Ɨ 1 0 ļŠ± ļŠØ ļŠ§ kgā‹…m/s
  • C 2 . 0 6 Ɨ 1 0 ļŠ± ļŠØ ļŠ§ kgā‹…m/s
  • D 3 . 2 4 Ɨ 1 0 ļŠ± ļŠØ ļŠ§ kgā‹…m/s
  • E 5 . 1 1 Ɨ 1 0 ļŠ± ļŠ§ ļŠŖ 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 . 2 9 Ɨ 1 0 ļŠ± ļŠØ ļŠ¬ kgā‹…m/s. Using the formula Ī” š‘„ Ī” š‘ ā‰„ ā„Ž 4 šœ‹ , calculate the minimum possible uncertainty in the position of the photon. Use a value of 6 . 6 3 Ɨ 1 0 ļŠ± 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 violet line
  • CThe blue line
  • DThe green line
  • EThe black line

Q8:

A proton moving through free space has an uncertainty in its momentum of 4 . 0 0 Ɨ 1 0 ļŠ± ļŠØ ļŠ® kgā‹…m/s. Using the formula Ī” š‘„ Ī” š‘ ā‰„ ā„Ž 4 šœ‹ , calculate the minimum possible uncertainty in the position of the proton. Use a value of 6 . 6 3 Ɨ 1 0 ļŠ± 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?

  • A Ī” š‘„ āˆ 1 Ī” š‘
  • B Ī” š‘„ āˆ Ī” š‘ ļŠØ
  • C Ī” š‘„ āˆ Ī” š‘ 2
  • D Ī” š‘„ āˆ 1 Ī” š‘ ļŠØ
  • E Ī” š‘„ āˆ Ī” š‘

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