# 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

**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 cubical container with a side length of 25.000 cm.

What is the minimum uncertainty in the momentum components of 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 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, min.

What is the value of min?

- 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 min?

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

- 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 min?