Calculating the Lifetime of J/ψ Meson Using the Uncertainty Principle

  • Context: Graduate 
  • Thread starter Thread starter airkapp
  • Start date Start date
  • Tags Tags
    Lifetime Meson
Click For Summary

Discussion Overview

The discussion revolves around estimating the lifetime of the J/ψ meson using the uncertainty principle, specifically focusing on the relationship between energy width and lifetime. Participants explore the calculations involved and clarify steps in the application of the uncertainty principle.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant introduces the problem of estimating the lifetime of the J/ψ meson using its measured width of 88 keV and the uncertainty principle, suggesting a lifetime of approximately 8E-21 s.
  • Another participant agrees with the approach and provides a similar estimate of ~7E-21 s, indicating the use of the uncertainty time-energy relation.
  • A participant requests further clarification on the steps to arrive at the estimate of 7E-21 s, indicating some confusion with the calculations.
  • One participant elaborates on the uncertainty relation, providing a detailed calculation that results in an estimate of approximately 3.74E-21 s, noting that the difference arises from using a specific form of the uncertainty relation.
  • A participant questions the use of 4π instead of 2π in the calculations, seeking clarification on this choice.
  • The responding participant explains that the factor comes from the relationship between h and ħ, specifically stating that ħ/2 = h/4π.

Areas of Agreement / Disagreement

Participants present differing estimates for the lifetime of the J/ψ meson, with one suggesting 8E-21 s and another providing a calculation that yields approximately 3.74E-21 s. There is no consensus on the correct value, and the discussion remains unresolved regarding the precise lifetime calculation.

Contextual Notes

The discussion includes assumptions about the applicability of the uncertainty principle and the specific constants used in calculations, which may influence the results. The differences in estimates highlight potential dependencies on the definitions and interpretations of the uncertainty relation.

airkapp
Messages
58
Reaction score
0
I'm just being introduced to particle physics and wondering if I'm going about this correct..can someone help me? thanks

The measured width of the J/ψ meson is 88 keV. Estimate its lifetime.

Lifetime (s) of J/ψ meson is 8E-21 s
Using uncertainty principle: ΔE = h/2πΔt isolate for delta t?
8E-21s – 5E-22s
= 7.5E-21 s ?
 
Last edited:
Physics news on Phys.org
Yes,u have to use the uncertainty time-energy...It should be ~[itex]7\cdot 10^{-21}s[/itex]

Daniel.
 
dextercioby said:
Yes,u have to use the uncertainty time-energy...It should be ~[itex]7\cdot 10^{-21}s[/itex]

Daniel.


thanks Daniel,

sorry to bother you again but do you think you can detail that out for me a little more..I think I'm having a little trouble following the steps of proportion to get [itex]7\cdot 10^{-21}s[/itex]

thanks
 
Okay.Assume the general uncertainty relation being satisfied in the equality limit also for time & energy (nice discussion on this relation,chapter 2 of [1]).

[tex]\Delta E\Delta t=\frac{\hbar}{2}[/tex]

Therefore

[tex]\Delta t=\frac{\hbar}{2\Delta E}\simeq\frac{6.626\cdot 10^{-34}\mbox{Js}}{4\pi\cdot 88\cdot 10^{3}\cdot 1.6\cdot 10^{-19}\mbox{J}}\simeq 3.74\cdot 10^{-21} \mbox{s}[/tex]

The difference from the prior result (post #2) comes from using [itex]=\frac{\hbar}{2}[/itex] instead of [itex]\approx\hbar[/itex] which is cusomery as well.


Daniel.


------------------------------------------------------
[1] J.J.Sakurai,"Modern Quantum Mechanics",any of the 2 editions.
 
Last edited:
Hmmmm,something weird here. The above message appears as unposted. :confused: Can anyone see it...?

Daniel.
 
dextercioby said:
Okay.Assume the general uncertainty relation being satisfied in the equality limit also for time & energy (nice discussion on this relation,chapter 2 of [1]).

[tex]\Delta E\Delta t=\frac{\hbar}{2}[/tex]

Therefore

[tex]\Delta t=\frac{\hbar}{2\Delta E}\simeq\frac{6.626\cdot 10^{-34}\mbox{Js}}{4\pi\cdot 88\cdot 10^{3}\cdot 1.6\cdot 10^{-19}\mbox{J}}\simeq 3.74\cdot 10^{-21} \mbox{s}[/tex]

The difference from the prior result (post #2) comes from using [itex]=\frac{\hbar}{2}[/itex] instead of [itex]\approx\hbar[/itex] which is cusomery as well.


Daniel.


------------------------------------------------------
[1] J.J.Sakurai,"Modern Quantum Mechanics",any of the 2 editions.

thankyou Daniel,

I see now. But why did you use 4pi instead of 2pi?

thanks,
Jason
 
It comes from
[tex]\frac{\hbar}{2}=\frac{h}{4\pi}[/tex].​


Daniel.
 

Similar threads

Uncertainty Principle and the lifetime of an excited state
  • · Replies 1 ·
Replies
1
Views
2K
Calculate the lifetime of the theta meson
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Progress In Calculating The HLbL Contribution To Muon g-2
  • · Replies 0 ·
Replies
0
Views
4K
Basic Energy and Time Uncertainty Problem
  • · Replies 2 ·
Replies
2
Views
3K
What is the Uncertainty in the Wavelength of Emitted Photon?
  • · Replies 5 ·
Replies
5
Views
19K
How Does LIGO Detect Gravitational Waves Using Laser Interferometry?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Estimating Mass Uncertainty of Mesons Using the Uncertainty Principle
  • · Replies 5 ·
Replies
5
Views
6K
Use the uncertainty principle for momentum vs. position to e
  • · Replies 2 ·
Replies
2
Views
2K
Use Uncertainty Principle to estimate the size of the H atom
  • · Replies 6 ·
Replies
6
Views
7K
Calculating Emitted Photon Properties for Excited Atoms | Homework Help
  • · Replies 10 ·
Replies
10
Views
2K