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 traveling at a speed of 5.000×10 m/s?

Q3:

What is the wavelength of an electron that is moving at a 3.00% 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 De Broglie wavelength of the proton.

Q6:

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

  • A2.38×10 m/s
  • B2.55×10 m/s
  • C2.70×10 m/s
  • D2.21×10 m/s
  • E2.06×10 m/s

Q7:

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

  • A1.06×10 m/s
  • B4.35×10 m/s
  • C4.22×10 m/s
  • D3.45×10 m/s
  • E2.11×10 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?

  • A11×10 m
  • B4.6×10 m
  • C7.7×10 m
  • D1.5×10 m
  • E23×10 m

Q11:

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

  • A0.313𝑐
  • B0.290𝑐
  • C0.228𝑐
  • D0.524𝑐
  • E0.145𝑐

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?

  • A5.71×10 J
  • B4.87×10 J
  • C2.37×10 J
  • D5.26×10 J
  • E3.33×10 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.

  • A6.67×10 kg⋅m/s
  • B1.25×10 kg⋅m/s
  • C1.18×10 kg⋅m/s
  • D5.00×10 kg⋅m/s
  • E6.25×10 kg⋅m/s

Find the velocity of the neutron with the same momentum.

What is the neutron’s kinetic energy?

  • A1.27×10 J
  • B4.84×10 J
  • C2.25×10 J
  • D1.33×10 J
  • E3.14×10 J

Q16:

A neutron has a wavelength of 5.60 fm.

What is the neutron’s velocity?

  • A19.0×10 m/s
  • B70.6×10 m/s
  • C69.0×10 m/s
  • D34.5×10 m/s
  • E96.0×10 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?

  • A1.53×10 m/s
  • B2.16×10 m/s
  • C5.49×10 m/s
  • D7.27×10 m/s
  • E3.45×10 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 2×10 m, small enough to detect details about one-tenth the size of a nucleon.

  • A9×10 J
  • B5×10 J
  • C10×10 J
  • D10×10 J
  • E9×10 J

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