# Worksheet: Matter Waves

In this worksheet, we will practice calculating the de Broglie wavelength of massive particles that have a given momentum or velocity.

Q1:

If an electron and a muon have the same speed, which particle has the greater de Broglie wavelength?

• AThe electron
• BThe muon

Q2:

Which of the following formulas shows the relation between the de Broglie wavelength of a particle, , its momentum , and the Planck constant ?

• A
• B
• C
• D
• E

Q3:

A muon has a rest mass of kg. If the muon is moving at a speed of 20 m/s, what is its de Broglie wavelength? Use a value of J⋅s for the Planck constant. Give your answer to 3 significant figures.

• A m
• B m
• C m
• D m
• E m

Q4:

An electron has a rest mass of kg. If the electron has a kinetic energy of J, what is its de Broglie wavelength? Use a value of J⋅s for the Planck constant. Give your answer to 3 significant figures.

• A m
• B m
• C m
• D m
• E m

Q5:

A proton has a rest mass of kg. At what speed would a proton have to move in order to have a de Broglie wavelength of m? Use a value of J⋅s for the Planck constant. Give your answer to 3 significant figures.

Q6:

What is the kinetic energy of a muon that has a de Broglie wavelength of m? Use a value of kg for the rest mass of a muon and a value of J⋅s for the Planck constant. Give your answer to 3 significant figures.

• A856 J
• B J
• C J
• D J
• E428 J

Q7:

A particle has a de Broglie wavelength of 0.200 nm. What is its momentum? 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

Q8:

What is the de Broglie wavelength of an electron that has a momentum of kg⋅m/s? Use a value of J⋅s for the Planck constant. Give your answer to 3 significant figures.

• A m
• B m
• C m
• D m
• E m

Q9:

If a muon and a proton have the same de Broglie wavelength, which particle has the greater speed?

• ABoth have equal speeds.
• BThe proton
• CThe muon

Q10:

In a nuclear fission reactor, the moderator is a material used to slow down the free neutrons in the reactor core, which increases the probability that they will cause a uranium nucleus to undergo fission. The neutrons must have kinetic energies of about 0.0400 eV. What is the de Broglie wavelength of a neutron with this kinetic energy? Use a value of kg for the rest mass of a neutron and a value of J⋅s for the Planck constant. Give your answer to 3 significant figures.

• A m
• B m
• C m
• D m
• E m

Q11:

The graph shows a number of curves. Which curve shows the relation between the momentum of a particle and its de Broglie wavelength? • AThe blue line
• BThe yellow line
• CThe purple line
• DThe red line
• EThe green line