# 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 m^{ā1}.
Use the formula to find
the minimum uncertainty in the position of the photon. Give your answer to 3
significant figures.

- A m
- B m
- C m
- D m
- E 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 to find the minimum uncertainty in the wavenumber of the photon. Give your answer to 3 significant figures.

- A
m
^{ā1} - B
m
^{ā1} - C
m
^{ā1} - D
m
^{ā1} - E
m
^{ā1}

**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 m. Using the formula , calculate the minimum possible uncertainty in the momentum of the electron. Use a value of for the Planck constant. Give your answer to 3 significant figures.

- A kgā m/s
- B kgā m/s
- C kgā m/s
- D kgā m/s
- E 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 kgā m/s. Using the formula , calculate the minimum possible uncertainty in the position of the photon. Use a value of 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 kgā m/s. Using the formula , calculate the minimum possible uncertainty in the position of the proton. Use a value of 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
- B
- C
- D
- E