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

• airkapp
In summary, the measured width of the J/ψ meson is 88 keV. Estimate its lifetime using the uncertainty principle. Lifetime (s) of J/ψ meson is 8E-21 s.
airkapp
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:
Yes,u have to use the uncertainty time-energy...It should be ~$7\cdot 10^{-21}s$

Daniel.

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

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 $7\cdot 10^{-21}s$

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]).

$$\Delta E\Delta t=\frac{\hbar}{2}$$

Therefore

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

The difference from the prior result (post #2) comes from using $=\frac{\hbar}{2}$ instead of $\approx\hbar$ 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. 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]).

$$\Delta E\Delta t=\frac{\hbar}{2}$$

Therefore

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

The difference from the prior result (post #2) comes from using $=\frac{\hbar}{2}$ instead of $\approx\hbar$ 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
$$\frac{\hbar}{2}=\frac{h}{4\pi}$$.​

Daniel.

What is the lifetime of a J/ψ meson?

The lifetime of a J/ψ meson is approximately 7.2 × 10^-21 seconds.

What factors contribute to the lifetime of a J/ψ meson?

The lifetime of a J/ψ meson is primarily determined by the strength of the strong nuclear force, which governs the interactions between quarks and antiquarks within the meson.

How is the lifetime of a J/ψ meson measured?

The lifetime of a J/ψ meson is typically measured using particle detectors such as the Large Hadron Collider (LHC) at CERN. These detectors track the decay products of the meson and use this information to calculate its lifetime.

How does the lifetime of a J/ψ meson compare to other subatomic particles?

The lifetime of a J/ψ meson is relatively short compared to other subatomic particles such as protons and neutrons, which have lifetimes on the order of 10^30 seconds.

Can the lifetime of a J/ψ meson be altered or manipulated?

The lifetime of a J/ψ meson is determined by fundamental physical laws and cannot be altered or manipulated by external factors.

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