Neutron and protons, bff's?

Classical Mechanics Level 4

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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