29.7 Probability: The Heisenberg Uncertainty Principle

(a) If the position of an electron in a membrane is measured to an accuracy of $1 . \text{00 }\mu\text{m}$, what is the electron’s minimum uncertainty in velocity? (b) If the electron has this velocity, what is its kinetic energy in eV? (c) What are the implications of this energy, comparing it to typical molecular binding energies?

Suppose the velocity of an electron in an atom is known to an accuracy of $2 . 0 \times \text{10}^{3} \text{ m}/\text{s}$ (reasonably accurate compared with orbital velocities). What is the electron’s minimum uncertainty in position, and how does this compare with the approximate 0.1-nm size of the atom?

A relatively long-lived excited state of an atom has a lifetime of 3.00 ms. What is the minimum uncertainty in its energy?

The decay energy of a short-lived particle has an uncertainty of 1.0 MeV due to its short lifetime. What is the smallest lifetime it can have?

What is the approximate uncertainty in the mass of a muon, as determined from its decay lifetime?