7.2 The Heisenberg Uncertainty Principle

Position-momentum and energy-time limits, their origin in wave-packet spreading, and estimating ground-state energies and spectral linewidths from them.

University Physics Volume 3, 7.2 The Heisenberg Uncertainty Principle

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6 exercises

7.2 Exercise 1

A sodium atom makes a transition from the first excited state to the ground state, emitting a 589.0-nm photon with energy 2.105 eV. If the lifetime of this excited state is $1.6 \times 10^{−8} \text{s}$ , what is the uncertainty in energy of this excited state? What is the width of the corresponding spectral line?

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7.2 Exercise 3

Can the de Broglie wavelength of a particle be known precisely? Can the position of a particle be known precisely?

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7.2 Exercise 5

Can we measure both the position and momentum of a particle with complete precision?

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7.2 Exercise 7

A gas of helium atoms at 273 K is in a cubical container with 25.0 cm on a side. (a) What is the minimum uncertainty in momentum components of helium atoms? (b) What is the minimum uncertainty in velocity components? (c) Find the ratio of the uncertainties in (b) to the mean speed of an atom in each direction.

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7.2 Exercise 9

Some unstable elementary particle has a rest energy of 80.41 GeV and an uncertainty in rest energy of 2.06 GeV. Estimate the lifetime of this particle.

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7.2 Exercise 11

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 2.1-eV photon. (a) Estimate the uncertainty in the frequency of the photon. (b) What fraction of the photon’s average frequency is this?

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