# 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.

**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

**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?

**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 0.020 around the given point ?

- A4.0%
- B5.1%
- C6.2%
- D1.1%
- E2.7%

What is the probability of finding the particle in a region of width 0.020 around the given point ?

- A2.3%
- B1.9%
- C1.4%
- D3.1%
- E2.7%

What is the probability of finding the particle in a region of width 0.020 around the given point ?

- A4.8%
- B4.0%
- C3.1%
- D6.2%
- E5.4%

What is the probability of finding the particle in a region of width 0.020 around the given point ?

- A1.9%
- B1.1%
- C2.5%
- D3.1%
- E1.4%