Estimating Mass Uncertainty of Mesons Using the Uncertainty Principle

[Arieniel]

Hello, I am in first year physics and I was wondering if anyone could help me out with a question. Its dealing with Heisenberg's Uncertainty prinicple:

A meson is an unstable particle produced in high-energy paritcle collisions. Its rest energy is about 135 MeV and it exisits for an average lifetime of only 8.70 x 10^-17 s before decaying into two gamma rays. Using the uncertainty principle, estimate the fractional uncertainty delta m/m in its mass determination.
thankyou ahead of time for the help !
Arieniel

 

[Doc Al]

One of the uncertainty relations is ΔE x ΔT > h-bar/2. (You can interpret the lifetime as the "uncertainty" in time.) Does that help?

And welcome to the Physics Forums, by the way!

 

[Arieniel]

Further Question

Thanks for welcoming me to board,
i know that there is an uncertainity equation of delta x delta p is >/ h/2
does this come into play and where does the energy come into play, because i found delta E

 

[Javier]

The uncertainty in the mass energy of this meson (mc^2) is related to the lifetime of the particle via:
{uncertainty in mc^(2)}*t ~ h-bar.

The reason this works is more subtle than your course goes into, but it has to do with the "cross section" that the particles see as they collide to create this short-lived particle. One can calculate the transition rate from the quantum state {collection of some particles} to the state where you have a meson, and this will depend on the range of energies for which this transition can happen (ie, the uncertainty in the energy to create the meson). The inverse of this transition rate is the lifetime of the meson. So you can see at least where the inverse relationship between the uncertainty in mass-energy of the meson and its lifetime.

 

[Doc Al]

The ΔE can be interpreted as the uncertainty in the meson's mass (rest energy). Express it in units of MeV.

Note: I was just struggling with a more complete answer, when I noticed that Javier beat me to it.

 

[Arieniel]

I sincerely thank you both! You have saved me from burning the midnight oil! I appreciate this greatly!

Cheers
Arieniel