Calculating the lifetime of a particle

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SUMMARY

The discussion focuses on calculating the lifetime of a Δ particle formed by a pi meson and a proton, with a measured energy peak of 1236 MeV and an experimental spread of 120 MeV. The relationship ΔE*Δt ~ h-bar is utilized to derive the lifetime, where ΔE is interpreted as the experimental spread. The proposed solution is to calculate the lifetime using the formula (h-bar)/(120 MeV), confirming that the experimental spread equates to ΔE.

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  • Understanding of quantum mechanics principles, particularly the uncertainty principle.
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  • Knowledge of energy measurements in particle physics, including concepts like rest energy.
  • Basic proficiency in using Planck's constant (h-bar) in calculations.
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  • Study the uncertainty principle in quantum mechanics to deepen understanding of ΔE and Δt relationships.
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Takuza
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1. Homework Statement

A pi meson (pion) and a proton can briefly join together to form a Δ particle. A measurement of the energy of the ∏p system shows a peak at 1236 MeV, corresponding to the rest energy of the Δ particle, with an experimental spread of 120 MeV. What is the lifetime of the Δ?
A graph is given of the reaction probability as a function of energy, peaking at energy 1236 MeV. There are arrows on both sides of the peak labeled 120 MeV.


2. Homework Equations

ΔE*Δt ~ h-bar


3. The Attempt at a Solution
I am mainly unsure as to what an experimental spread is. My guess is that the experimental spread is equal to ΔE, and so the solution is simply (h-bar)/(120MeV), but that seems too simple.
 
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Hi Takuza! :wink:
Takuza said:
A pi meson (pion) and a proton can briefly join together to form a Δ particle. A measurement of the energy of the ∏p system shows a peak at 1236 MeV, corresponding to the rest energy of the Δ particle, with an experimental spread of 120 MeV. What is the lifetime of the Δ?

I am mainly unsure as to what an experimental spread is. My guess is that the experimental spread is equal to ΔE, and so the solution is simply (h-bar)/(120MeV), but that seems too simple.

Yup … "experimental spread" and "uncertainty" seem to mean the same :smile:
 

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