# Neutron and protons, bff's?

The bond between protons and neutrons inside the atomic nucleus is formed by the strong interaction. In classical terms, we can think of it as protons and neutrons exchanging a "meson," a kind of fundamental particle between them. Let's estimate the range of the interaction that's caused by exchange of the $$\pi$$ meson which has mass of approximately $$2.5 \times 10^{-28}~\mbox{kg}$$ and decays. To do this, note that from the uncertainty principle one can estimate the lifetime $$t$$ of a particle of mass $$m$$ by $$t=\frac{\hbar}{2mc^2}$$, where $$\hbar=1.05 \times 10^{-34} ~\mbox{J~s}$$ is known as the (reduced) Planck's constant and $$c=3 \times 10^8 ~\mbox{m/s}$$ is the speed of light.

Express your answer in femtometers $$1~\mbox{fm}=10^{-15}~\mbox{m}$$.

Details and assumptions

• Nothing can travel faster than the speed of light.
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