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 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 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
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

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