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Worksheet: Heisenberg's Uncertainty Principle

Q1:

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 2 . 3 8 × 1 0 3 4 N⋅s
  • B 1 . 8 9 × 1 0 3 4 N⋅s
  • C 2 . 6 2 × 1 0 3 4 N⋅s
  • D 2 . 1 1 × 1 0 3 4 N⋅s
  • E 2 . 8 8 × 1 0 3 4 N⋅s

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

  • A 6 . 3 1 × 1 0 8 m/s
  • B 5 . 7 7 × 1 0 8 m/s
  • C 5 . 2 1 × 1 0 8 m/s
  • D 4 . 8 2 × 1 0 8 m/s
  • E 6 . 9 3 × 1 0 8 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 7 . 2 5 × 1 0 1 1 1
  • B 6 . 2 3 × 1 0 1 1 1
  • C 5 . 9 4 × 1 0 1 1 1
  • D 6 . 5 6 × 1 0 1 1 1
  • E 6 . 8 9 × 1 0 1 1 1

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 1 . 5 1 × 1 0 2 5 s
  • B 1 . 3 9 × 1 0 2 5 s
  • C 1 . 6 9 × 1 0 2 5 s
  • D 1 . 6 0 × 1 0 2 5 s
  • E 1 . 8 0 × 1 0 2 5 s

Q3:

Use the Heisenberg uncertainty principle to calculate the uncertainty in energy for a corresponding time interval of 5 . 3 9 × 1 0 4 4 s.

  • A 9 . 1 1 × 1 0 1 8 GeV
  • B 6 . 8 3 × 1 0 1 8 GeV
  • C 1 . 4 3 × 1 0 1 9 GeV
  • D 3 . 8 4 × 1 0 1 9 GeV
  • E 5 . 0 6 × 1 0 1 9 GeV

Q4:

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 3 . 1 4 × 1 0 9
  • B 3 . 8 1 × 1 0 9
  • C 2 . 5 8 × 1 0 9
  • D 1 . 8 6 × 1 0 9
  • E 4 . 4 9 × 1 0 9