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, 𝜆, its momentum 𝑝, and the Planck constant ℎ?

  • A𝜆=ℎ𝑝
  • B𝜆=ℎ𝑝
  • C𝜆=ℎ𝑝
  • D𝜆=𝑝ℎ
  • E𝜆=ℎ𝑝

Q3:

A muon has a rest mass of 1.89×10 kg. If the muon is moving at a speed of 20 m/s, what is its de Broglie wavelength? Use a value of 6.63×10 J⋅s for the Planck constant. Give your answer to 3 significant figures.

  • A2.51×10 m
  • B1.75×10 m
  • C4.64×10 m
  • D5.70×10 m
  • E8.60×10 m

Q4:

An electron has a rest mass of 9.11×10 kg. If the electron has a kinetic energy of 1.14×10 J, what is its de Broglie wavelength? Use a value of 6.63×10 J⋅s for the Planck constant. Give your answer to 3 significant figures.

  • A2.90×10 m
  • B4.11×10 m
  • C1.45×10 m
  • D1.03×10 m
  • E2.06×10 m

Q5:

A proton has a rest mass of 1.67×10 kg. At what speed would a proton have to move in order to have a de Broglie wavelength of 8.82×10 m? Use a value of 6.63×10 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 4.10×10 m? Use a value of 1.89×10 kg for the rest mass of a muon and a value of 6.63×10 J⋅s for the Planck constant. Give your answer to 3 significant figures.

  • A856 J
  • B9.78×10 J
  • C1.38×10 J
  • D6.92×10 J
  • E428 J

Q7:

A particle has a de Broglie wavelength of 0.200 nm. What is its momentum? Use a value of 6.63×10 J⋅s for the Planck constant. Give your answer to 3 significant figures.

  • A1.66×10 kg⋅m/s
  • B3.02×10 kg⋅m/s
  • C3.32×10 kg⋅m/s
  • D4.55×10 kg⋅m/s
  • E1.33×10 kg⋅m/s

Q8:

What is the de Broglie wavelength of an electron that has a momentum of 4.56×10 kg⋅m/s? Use a value of 6.63×10 J⋅s for the Planck constant. Give your answer to 3 significant figures.

  • A6.88×10 m
  • B1.04×10 m
  • C3.02×10 m
  • D1.45×10 m
  • E2.11×10 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 1.67×10 kg for the rest mass of a neutron and a value of 6.63×10 J⋅s for the Planck constant. Give your answer to 3 significant figures.

  • A7.17×10 m
  • B2.03×10 m
  • C1.43×10 m
  • D2.86×10 m
  • E1.01×10 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

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