(a) In a typical nucleus, a neutron is confined within a space on the order of 10-15 m. What is the minimum uncertainty in the momentum of such a neutron? (b) A free neutron decays into a proton, electron and anti-neutrino with a half-life of about 10 minutes. Using the time-energy uncertainty principle and Einstein’s equation relating mass and energy, determine the uncertainty in the mass of a free neutron (give your answer in atomic mass units).
Added by Dawn R.
Close
Step 1
626 x 10^-34 J s) and Δx is the confinement space (10^-15 m). Plugging in the values: Δp = (6.626 x 10^-34) / (4π * 10^-15) Δp = 5.27 x 10^-20 kg m/s Show more…
Show all steps
Your feedback will help us improve your experience
Penny Riley and 92 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A free neutron (that is, a neutron on its own rather than in a nucleus) is not a stable particle. Its average lifetime is $15 \mathrm{~min}$, after which it decays into a proton, an electron, and an antineutrino. Use the energy-time uncertainty principle [Eq. $(28-3)]$ and the relationship between mass and rest energy to estimate the inherent uncertainty in the mass of a free neutron. Compare to the average neutron mass of $1.67 \times 10^{-27} \mathrm{~kg}$. (While 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.)
A free neutron is confined to a one-dimensional region of typical nuclear dimension L = 10.0 fm. Estimate the minimum uncertainty Δv in the neutron's velocity. Δv = 3.16 x 10^6 m/s Use Heisenberg's uncertainty principle to estimate the neutron's kinetic energy K. K = 8.35 x 10^-15 J Estimate the minimum kinetic energy K3D if the region is three-dimensional. K3D = 8.22 x 10^-14 J
Timothy J.
A free neutron beta decays by creating a proton, an electron, and an antineutrino according to the reaction $\mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{-}+\bar{\nu} .$ Imagine that a free neutron were to decay by creating a proton and electron according to the reaction $$\mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{-}$$ and assume that the neutron is initially at rest in the laboratory. (a) Determine the energy released in this reaction. (b) Determine the speeds of the proton and electron after the reaction. (Energy and momentum are conserved in the reaction.) (c) Is either of these particles moving at a relativistic speed? Explain.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD