# Lifetime of J/ψ meson - easy

1. Apr 24, 2005

### 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: Apr 24, 2005
2. Apr 24, 2005

### dextercioby

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

Daniel.

3. Apr 24, 2005

### airkapp

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

4. Apr 24, 2005

### dextercioby

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: Apr 24, 2005
5. Apr 24, 2005

### dextercioby

Hmmmm,something weird here. :grumpy: The above message appears as unposted. Can anyone see it...?

Daniel.

6. Apr 24, 2005

### airkapp

thankyou Daniel,

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

thanks,
Jason

7. Apr 24, 2005

### dextercioby

It comes from
$$\frac{\hbar}{2}=\frac{h}{4\pi}$$.​

Daniel.