# Energy width of ground state neutral pion

1. Nov 8, 2009

### joeybenn

1. The problem statement, all variables and given/known data

Most of the particles known in physics are unstable. For example, the lifetime of the neutral pion, $$\pi^{0}$$, is about 1.0 x $$10^{-16}$$ s. Its mass is 1.35 x $$10^{8}$$ $$\frac{eV}{c^{2}}$$. What is the energy width of the $$\pi^{0}$$ in its ground state.

2. Relevant equations

$$\Delta E$$$$\Delta t$$ = $$\frac{h_{bar}}{2}$$

$$E_{n}$$= $$\frac{n^{2}h^{2}}{8ml^{2}}$$

3. The attempt at a solution

I was thinking of just putting the time into $$\Delta E$$$$\Delta t$$ = $$\frac{h_{bar}}{2}$$ and solving for $$\Delta E$$ but that seems too easy.

Could I find the length and of the pion and use $$E_{n}$$= $$\frac{n^{2}h^{2}}{8ml^{2}}$$ ?

I guess I am a little stumped at the moment.

BTW: I am not asking for an answer, just guidance.

Last edited: Nov 8, 2009
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