# 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 m/s?

Q3:

What is the wavelength of an electron that is moving at a 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 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?

• A m/s
• B m/s
• C m/s
• D m/s
• E m/s

Q7:

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

• A m/s
• B m/s
• C m/s
• D m/s
• E 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 m
• B m
• C m
• D m
• E m

Q11:

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

• A
• B
• C
• D
• E

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 J
• B J
• C J
• D J
• E 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 kg⋅m/s
• B kg⋅m/s
• C kg⋅m/s
• D kg⋅m/s
• E kg⋅m/s

Find the velocity of the neutron with the same momentum.

What is the neutron’s kinetic energy?

• A J
• B J
• C J
• D J
• E J

Q16:

A neutron has a wavelength of 5.60 fm.

What is the neutron’s velocity?

• A m/s
• B m/s
• C m/s
• D m/s
• E 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 m/s
• B m/s
• C m/s
• D m/s
• E 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 m, small enough to detect details about one-tenth the size of a nucleon.

• A J
• B J
• C J
• D J
• E J