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In this lesson, we will learn how to calculate the energy, duration of existence, momentum, and position of particles using the Heisenberg 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?

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

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

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?

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.

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?

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