Calculate the lifetime of the theta meson

[FateEternal]

A newly discovered Θ meson has a rest mass energy of 1020 MeV, and electric charge of 0, and a measured energy width of 4 MeV

a Using the uncertainty principle, calculate the lifetime of the Θ meson

b A Θ meson at rest decays into K+ and K- mesons. Find the total KE of the kaons

Thanks
and if you can also help explain the uncertainty principle

 

[fargoth]

the uncertainty principle stems fromthe fact every particle is described by a wave packet of probability density.
the wave-number (k=\frac{2 \pi}{\lambda}) of this packet is the momentum.
when you try to make a wave packet defined in space, you need to add lots of monochromatic waves with different wave-numbers togethere - and when you got only one monochromatic wave (meaning there is only one wave-number) the wave looks like a sine which comes from minus infinity and continues to infinity. meaning you got undefined coordinates for the particle..
so the particle can be described as
\Psi (x)=\Sigma C_ne^{ik_nx}
by using Fourier transform from x to k (when given the shape of particle packet in space) you could see that the minimum value of \Delta x\Delta p=\frac{1}{2}
(when \hbar=1, not in cgs)
energy and time are related to each other the same way as space and momentum, since a Fourier transform of x to t when \Psi (x)=\Sigma C_ne^{ik_nx} will give you the \Psi (t)=\Sigma U_ne^{iE_nt}
so if you know the energy width of the particle, youd know the time width.
by \Delta E\Delta t >= \frac{\hbar}{2} in cgs.
if you want more info look here http://zebu.uoregon.edu/~js/21st_century_science/lectures/lec14.html

 

[FateEternal]

wouldnt it be ^E^t>h/2pi?

 

[fargoth]

well, \hbar=\frac{h}{2\pi}
so it would be greater then \frac{h}{4\pi}
but \Delta x\Delta p roughly equals to \frac{h}{2\pi}