Question

A subatomic particle created in an experiment exists in a certain state for a time of $\Delta t=7.4 \times 10^{-20} \mathrm{~s}$ before decaying into other particles. Apply both the Heisenberg uncertainty principle and the equivalence of energy and mass (see Section 28.6) to determine the minimum uncertainty involved in measuring the mass of this shortlived particle.

Name: Problem 42, Chapter 29: Physics
Uploaded: 2021-12-02T22:59:16-08:00
Duration: 1 min 49 s
Channel: Suzanne W.
Description: A subatomic particle created in an experiment exists in a certain state for a time of Δt=7.4 ×10^-20 s before decaying into other particles. Apply both the Heisenberg uncertainty principle and the equivalence of energy and mass (see Section 28.6) to determine the minimum uncertainty involved in measuring the mass of this shortlived particle.

   A subatomic particle created in an experiment exists in a certain state for a time of $\Delta t=7.4 \times 10^{-20} \mathrm{~s}$ before decaying into other particles. Apply both the Heisenberg uncertainty principle and the equivalence of energy and mass (see Section 28.6) to determine the minimum uncertainty involved in measuring the mass of this shortlived particle.

Physics

John D. Cutnell,… 8th Edition

Chapter 29, Problem 42

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Solved by Expert Suzanne W.

12/02/2021

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Mathematically, this is represented as: \[\Delta E \Delta t \approx \frac{\hbar}{4\pi}\] Show more…

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A subatomic particle created in an experiment exists in a certain state for a time of $\Delta t=7.4 \times 10^{-20} \mathrm{~s}$ before decaying into other particles. Apply both the Heisenberg uncertainty principle and the equivalence of energy and mass (see Section 28.6) to determine the minimum uncertainty involved in measuring the mass of this shortlived particle.

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Key Concepts

Heisenberg Uncertainty Principle

This principle states that certain pairs of physical properties, such as energy and time, cannot both be measured exactly, at the same time. In the context of particle physics, if a subatomic particle has a very short lifetime, there is an inherent uncertainty in its energy, meaning that a precise measurement of its energy (and hence its mass) is fundamentally limited.

Mass-Energy Equivalence

Mass-energy equivalence, encapsulated by Einstein’s equation E=mc², indicates that mass can be understood as a form of energy. This relationship allows one to convert the uncertainty in energy, as given by the Heisenberg uncertainty principle, into an uncertainty in mass, providing a direct link between the lifetime of a particle and the precision with which its mass can be measured.

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