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 muon
  • BThe electron

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 ?

  • A 𝜆 = ℎ 𝑝 
  • B 𝜆 = ℎ 𝑝
  • C 𝜆 = ℎ 𝑝 
  • D 𝜆 = ℎ 𝑝  
  • E 𝜆 = 𝑝 ℎ

Q3:

A muon has a rest mass of 1 . 8 9 × 1 0    kg. If the muon is moving at a speed of 20 m/s, what is its de Broglie wavelength? Use a value of 6 . 6 3 × 1 0    J⋅s for the Planck constant. Give your answer to 3 significant figures.

  • A 1 . 7 5 × 1 0   m
  • B 4 . 6 4 × 1 0   m
  • C 8 . 6 0 × 1 0   m
  • D 2 . 5 1 × 1 0    m
  • E 5 . 7 0 × 1 0  m

Q4:

An electron has a rest mass of 9 . 1 1 × 1 0    kg. If the electron has a kinetic energy of 1 . 1 4 × 1 0    J, what is its de Broglie wavelength? Use a value of 6 . 6 3 × 1 0    J⋅s for the Planck constant. Give your answer to 3 significant figures.

  • A 2 . 9 0 × 1 0   m
  • B 2 . 0 6 × 1 0   m
  • C 1 . 4 5 × 1 0   m
  • D 1 . 0 3 × 1 0   m
  • E 4 . 1 1 × 1 0   m

Q5:

A proton has a rest mass of 1 . 6 7 × 1 0    kg. At what speed would a proton have to move in order to have a de Broglie wavelength of 8 . 8 2 × 1 0   m? Use a value of 6 . 6 3 × 1 0    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 . 1 0 × 1 0   m? Use a value of 1 . 8 9 × 1 0    kg for the rest mass of a muon and a value of 6 . 6 3 × 1 0    J⋅s for the Planck constant. Give your answer to 3 significant figures.

  • A 1 . 3 8 × 1 0    J
  • B 428 J
  • C 6 . 9 2 × 1 0    J
  • D 9 . 7 8 × 1 0    J
  • E 856 J

Q7:

A particle has a de Broglie wavelength of 0.200 nm. What is its momentum? Use a value of 6 . 6 3 × 1 0    J⋅s for the Planck constant. Give your answer to 3 significant figures.

  • A 3 . 3 2 × 1 0    kg⋅m/s
  • B 3 . 0 2 × 1 0   kg⋅m/s
  • C 4 . 5 5 × 1 0   kg⋅m/s
  • D 1 . 6 6 × 1 0    kg⋅m/s
  • E 1 . 3 3 × 1 0    kg⋅m/s

Q8:

What is the de Broglie wavelength of an electron that has a momentum of 4 . 5 6 × 1 0    kg⋅m/s? Use a value of 6 . 6 3 × 1 0    J⋅s for the Planck constant. Give your answer to 3 significant figures.

  • A 3 . 0 2 × 1 0    m
  • B 1 . 0 4 × 1 0   m
  • C 2 . 1 1 × 1 0    m
  • D 6 . 8 8 × 1 0  m
  • E 1 . 4 5 × 1 0   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 . 6 7 × 1 0    kg for the rest mass of a neutron and a value of 6 . 6 3 × 1 0    J⋅s for the Planck constant. Give your answer to 3 significant figures.

  • A 1 . 0 1 × 1 0    m
  • B 1 . 4 3 × 1 0    m
  • C 7 . 1 7 × 1 0    m
  • D 2 . 0 3 × 1 0    m
  • E 2 . 8 6 × 1 0    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 red line
  • BThe green line
  • CThe yellow line
  • DThe blue line
  • EThe purple line

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.