# 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