# Calculate the lifetime of the theta meson

1. Jan 15, 2006

### 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

2. Jan 15, 2006

### 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.

Last edited by a moderator: May 2, 2017
3. Jan 15, 2006

### FateEternal

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

4. Jan 19, 2006

### 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 $$\frac{h}{2\pi}$$