# Worksheet: Heisenberg's Uncertainty Principle

In this worksheet, we will practice calculating the energy, duration of existence, momentum, and position of particles using the Heisenberg uncertainty principle.

Q1:

Use the Heisenberg uncertainty principle to calculate the uncertainty in energy for a corresponding time interval of s.

• A GeV
• B GeV
• C GeV
• D GeV
• E GeV

Q2:

An unstable elementary particle has a rest energy of 80.41 GeV and an uncertainty in rest energy of 2.06 GeV. What is the minimum lifetime of this particle?

• A s
• B s
• C s
• D s
• E s

Q3:

Measurements indicate that an atom remains in an excited state for an average time of 50.0 ns before making a transition to the ground state with the simultaneous emission of a 2.10 eV photon.

What is the minimum uncertainty in the frequency of the emitted photon?

What fraction of the emitted photon’s average frequency is the minimum uncertainty in its frequency?

• A
• B
• C
• D
• E

Q4:

A gas of helium atoms at a temperature of 273 K is in a cubic container with sides of length 25.000 cm.

What is the minimum uncertainty in the momentum components of the helium atoms?

• A N⋅s
• B N⋅s
• C N⋅s
• D N⋅s
• E N⋅s

What is the minimum uncertainty in the velocity components of the helium atoms?

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

What is the ratio of the minimum uncertainty in the velocity components of the helium atoms to the mean speed of the atoms?

• A
• B
• C
• D
• E

Q5:

An atom in a metastable state has a lifetime of 4.2 ms. Find the minimum uncertainty in the measurement of the energy of the excited state.

• A J
• B J
• C J
• D J
• E J

Q6:

An electron is confined to a region of length 0.12 nm and its kinetic energy is equal to the ground state energy of the hydrogen atom in Bohr’s model, 13.6 eV. The electron has a minimum uncertainty in momentum, .

What is the value of ?

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

What fraction of the electron’s momentum is ?

What would the uncertainty in kinetic energy of this electron be if its momentum were equal to ?

• A J
• B J
• C J
• D J
• E J

What fraction of an electron’s kinetic energy is the minimum uncertainty in its kinetic energy if the momentum of the electron was equal to ?

Q7:

The mass of a -meson is measured to be 770 MeV/c2 with an uncertainty of 150 MeV/c2. Calculate the lifetime of this meson.

• A s
• B s
• C s
• D s
• E s

Q8:

A velocity measurement of an particle has been performed with a precision of 0.0100 mm/s. What is the minimum uncertainty in its position?

• A m
• B m
• C m
• D m
• E m

Q9:

The uncertainty in the -component of a proton’s position is 3.00 pm.

Find the minimum uncertainty in the simultaneous measurement of the proton’s -component of velocity.

• A m/s
• B10.5 m/s
• C m/s
• D m/s
• E m/s

Find the minimum uncertainty in the simultaneous measurement of the proton’s -component of velocity given that uncertainty about its -position is infinity.

• AIt cannot be determined.
• BThe minimum uncertainty in the simultaneous measurement of the proton’s -component of velocity is 0.
• CThe minimum uncertainty in the simultaneous measurement of the proton’s -component of velocity is infinity.
• DThe minimum uncertainty in the simultaneous measurement of the proton’s -component of velocity is .
• EThe minimum uncertainty in the simultaneous measurement of the proton’s -component of velocity is 1.

Q10:

A particle of mass is confined to a box of width . The particle is in the first excited state.

What is the probability of finding the particle in a region of width around the given point ?

• A
• B
• C
• D
• E

What is the probability of finding the particle in a region of width around the given point ?

• A
• B
• C
• D
• E

What is the probability of finding the particle in a region of width around the given point ?

• A
• B
• C
• D
• E

What is the probability of finding the particle in a region of width around the given point ?

• A
• B
• C
• D
• E