# 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−1. 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 .

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

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−1
• B m−1
• C m−1
• D m−1
• E m−1

Q4:

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

• Bincreases, increases
• Cdecreases, decreases

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 kg⋅m/s
• B kg⋅m/s
• C kg⋅m/s
• D kg⋅m/s
• E kg⋅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 kg⋅m/s. Using the formula , calculate the minimum possible uncertainty in the position of the photon. Use a value of J⋅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 kg⋅m/s. Using the formula , calculate the minimum possible uncertainty in the position of the proton. Use a value of J⋅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

Q10:

A muon that is produced 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 muon. Use a value of J⋅s for the Planck constant. Give your answer to 3 significant figures.

• A kg⋅m/s
• B kg⋅m/s
• C kg⋅m/s
• D kg⋅m/s
• E kg⋅m/s