A free neutron (i.e., a neutron on its own rather than in a...

A free neutron (i.e., a neutron on its own rather than in a nucleus) is not a stable particle. Its average lifetime is 15 min, after which it decays into a proton, an electron, and an antineutrino. Use the energy-time uncertainty principle [Eq. (28-5)] and the relationship between mass and rest energy to estimate the inherent uncertainty in the mass of a free neutron. Compare with the average neutron mass of $1.67 \times 10^{-27} \mathrm{kg} .$ (Although the uncertainty in the neutron's mass is far too small to be measured, unstable particles with extremely short lifetimes have marked variation in their measured masses.)

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Energy–Time Uncertainty Principle

This principle, a cornerstone of quantum mechanics, asserts that the uncertainty in energy (?E) and the uncertainty or duration of time (?t) are related by ?E?t ? ?/2. It implies that when a particle has a very short lifetime (small ?t), there is an inherently large uncertainty in its energy. This concept is crucial for understanding phenomena such as the spread in the mass of unstable particles.

Mass–Energy Equivalence

Mass–energy equivalence, expressed by Einstein’s famous equation E = mc², indicates that mass is a form of energy. Thus, any uncertainty in a particle’s energy directly translates into an uncertainty in its mass. This relationship is key when connecting the energy spread due to quantum uncertainties with variations in measured particle mass.

Particle Decay and Lifetime

In the context of unstable particles, such as free neutrons, the finite lifetime (or decay time) introduces an inherent uncertainty in energy due to the energy–time uncertainty principle. This energy uncertainty, when converted into a mass uncertainty via mass–energy equivalence, explains why the mass of decaying particles is not measured as a perfectly constant value, but rather exhibits a natural spread or uncertainty.

Transcript

Please give Ace some feedback