# General physics question involving Heisenberg Uncertainty Principle [closed]

Question:

An unstable particle produced in a high-energy collision is measured to have an energy of $483\ \mathrm{MeV}$ and an uncertainty in energy of $84\ \mathrm{keV}$. Use the Heisenberg uncertainty principle to estimate the lifetime of this particle.

Attempt at answer: I thought $$(\Delta E)(\Delta t) = \hbar = 1.055 \times 10^{-34}\ \mathrm{J}\cdot\mathrm{s} = 6.591 \times 10^{-16} \mathrm{eV}.$$

So I tried solving for $\Delta t$, my time, with $\Delta E = 84\ \mathrm{keV}$. However, this answer is wrong (I get something like $7.85 \times 10^{-21}\ \mathrm{s}$, which is incorrect). I assume I'm supposed to incorporate $483\ \mathrm{MeV}$ somehow, but am not sure how. Any suggestions?

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Hi user23254, and welcome to Physics Stackexchange. I added the homework tag appropriate for problems where guidance is better than straight-up answers. Also note that we support LaTeX-style markup to make things easier to read - you can see how I formatted the equations by editing the post. –  Chris White Apr 17 at 3:50
Your calculation looks OK to me. What answer were you expecting to get? –  John Rennie Apr 17 at 9:25