Worksheet: De Broglie Waves

In this worksheet, we will practice calculating the de Broglie wavelength of high-energy particles and macroscopic objects.

Q1:

What is the de Broglie wavelength of a proton whose kinetic energy is 2.0 MeV?

Q2:

What is the de Broglie wavelength of an electron travelling at a speed of 5 . 0 0 0 × 1 0 m/s?

Q3:

What is the wavelength of an electron that is moving at a 3 . 0 0 % of the speed of light?

Q4:

What is the de Broglie wavelength of a proton whose kinetic energy is 10 MeV?

Q5:

A proton in an accelerator has an energy of 1.00-TeV.

Find the Lorentz factor 𝛾 for the proton.

Find the DeBroglie wavelength for the proton.

Q6:

What is the velocity of a 0.400-kg billiard ball if its wavelength is 7.50 fm?

  • A 2 . 2 1 × 1 0 m/s
  • B 2 . 7 0 × 1 0 m/s
  • C 2 . 3 8 × 1 0 m/s
  • D 2 . 0 6 × 1 0 m/s
  • E 2 . 5 5 × 1 0 m/s

Q7:

At what velocity will an electron have a wavelength of 2.11 m?

  • A 3 . 4 5 × 1 0 m/s
  • B 4 . 2 2 × 1 0 m/s
  • C 1 . 0 6 × 1 0 m/s
  • D 4 . 3 5 × 1 0 m/s
  • E 2 . 1 1 × 1 0 m/s

Q8:

What is the kinetic energy of a 0.0300 nm wavelength electron in a tunneling electron microscope?

Q9:

What is the wavelength of an electron accelerated from rest by a 36.7 keV potential difference?

Q10:

What is the de Broglie wavelength of a 70 kg football player running at a speed of 6.5 m/s?

  • A 7 . 7 × 1 0 m
  • B 1 1 × 1 0 m
  • C 4 . 6 × 1 0 m
  • D 2 3 × 1 0 m
  • E 1 . 5 × 1 0 m

Q11:

At what velocity does a proton with a 5.80 fm wavelength move? Give your answer in units of 𝑐 .

  • A 0 . 3 1 3 𝑐
  • B 0 . 2 2 8 𝑐
  • C 0 . 2 9 0 𝑐
  • D 0 . 1 4 5 𝑐
  • E 0 . 5 2 4 𝑐

Q12:

Find the wavelength of a proton that is movingv at 3.40% of the speed of light.

Q13:

What is the de Broglie wavelength of an electron that is accelerated from rest through a potential difference of 16 keV?

Q14:

The de Broglie wavelength of a neutron is 0.0500 nm.

What is the speed of this neutron?

What is the energy of this neutron?

  • A 2 . 3 7 × 1 0 J
  • B 4 . 8 7 × 1 0 J
  • C 5 . 7 1 × 1 0 J
  • D 5 . 2 6 × 1 0 J
  • E 3 . 3 3 × 1 0 J

Q15:

An X-ray photon has an energy of 125 keV, and a neutron has the same momentum as the photon.

Find the momentum of the photon.

  • A 6 . 2 5 × 1 0 kg⋅m/s
  • B 5 . 0 0 × 1 0 kg⋅m/s
  • C 1 . 1 8 × 1 0 kg⋅m/s
  • D 6 . 6 7 × 1 0 kg⋅m/s
  • E 1 . 2 5 × 1 0 kg⋅m/s

Find the velocity of the neutron with the same momentum.

What is the neutron’s kinetic energy?

  • A 3 . 1 4 × 1 0 J
  • B 1 . 2 7 × 1 0 J
  • C 2 . 2 5 × 1 0 J
  • D 4 . 8 4 × 1 0 J
  • E 1 . 3 3 × 1 0 J

Q16:

A neutron has a wavelength of 5.60 fm.

What is the neutron’s velocity?

  • A 6 9 . 0 × 1 0 m/s
  • B 1 9 . 0 × 1 0 m/s
  • C 3 4 . 5 × 1 0 m/s
  • D 9 6 . 0 × 1 0 m/s
  • E 7 0 . 6 × 1 0 m/s

What is the neutron’s kinetic energy?

Q17:

A 45 GeV electron is produced in a linear accelerator. What is the wavelength of the electron?

Q18:

At what velocity will an electron have a wavelength of 2.11 m?

  • A 5 . 4 9 × 1 0 m/s
  • B 1 . 5 3 × 1 0 m/s
  • C 3 . 4 5 × 1 0 m/s
  • D 2 . 1 6 × 1 0 m/s
  • E 7 . 2 7 × 1 0 m/s

Q19:

The detail that you can observe using a probe is limited by its wavelength. Calculate the energy, in joules, of a particle that has a wavelength of 2 × 1 0 m, small enough to detect details about one-tenth the size of a nucleon.

  • A 1 0 × 1 0 J
  • B 9 × 1 0 J
  • C 9 × 1 0 J
  • D 5 × 1 0 J
  • E 1 0 × 1 0 J

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