(a) The measured width in the rest energy of the ψ(3097) meson is Γ=0.068 MeV. What is this meso

Name: Problem 28, Chapter 18: Modern Physics
Uploaded: 2021-11-26T06:19:09-08:00
Duration: 53 s
Channel: Chai Santi
Description: (a) The measured width in the rest energy of the ψ(3097) meson is Γ=0.068 MeV. What is this meson's mean lifetime? (b) What is the mean life of the ∑(1385) baryon, for which Γ=37 MeV ?

step 1 So first we have known that the mean lifetime is given by tau and it is hbar divided by tau and

Question

(a) The measured width in the rest energy of the $\psi(3097)$ meson is $\Gamma=0.068 \mathrm{MeV}$. What is this meson's mean lifetime? (b) What is the mean life of the $\sum(1385)$ baryon, for which $\Gamma=37 \mathrm{MeV} ?$

   (a) The measured width in the rest energy of the $\psi(3097)$ meson is $\Gamma=0.068 \mathrm{MeV}$. What is this meson's mean lifetime? (b) What is the mean life of the $\sum(1385)$ baryon, for which $\Gamma=37 \mathrm{MeV} ?$

Modern Physics

John R. Taylor,… 2nd Edition

Chapter 18, Problem 28

Instant Answer

Solved by Expert Chai Santi

11/26/2021

Step 1

Mathematically, this is represented as $\Delta E \Delta t \approx \hbar$, where $\Delta E$ is the uncertainty in energy, $\Delta t$ is the uncertainty in time, and $\hbar$ is the reduced Planck's constant. Show more…

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(a) The measured width in the rest energy of the $\psi(3097)$ meson is $\Gamma=0.068 \mathrm{MeV}$. What is this meson's mean lifetime? (b) What is the mean life of the $\sum(1385)$ baryon, for which $\Gamma=37 \mathrm{MeV} ?$

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Key Concepts

Heisenberg Energy-Time Uncertainty Principle

This principle establishes a fundamental limit to the precision with which energy and time can be simultaneously known in a quantum system. In the context of particle decay, it leads to the relation ? ? ?/?, where ? is the mean lifetime and ? is the energy width (or decay width) of the particle. The shorter the lifetime of the state, the greater the uncertainty in its energy, and vice versa.

Decay Width (?)

The decay width, often represented by the symbol ?, quantifies the range of energy values (i.e., the spread in energy) around the resonance mass of an unstable particle, reflecting its inherent instability. A larger decay width indicates a shorter mean lifetime, as the particle decays more rapidly, while a smaller width corresponds to a longer-lived state.

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