Minimum kinetic energy of a particle

Make an order of magnitude estimate of the kinetic energy of an alpha particle (a cluster of 2 protons + 2 neutrons) in a nucleus. Do not use SI units.

Heisenberg’s Uncertainty Principle says Δp Δx = /2. The alpha particle is confined to a nucleus so Δx is the size of a nucleus and we can therefore find a minimum momentum from this uncertainty principle.

Finally we can sub this approximate value into the equation for kinetic energy (the mass of an alpha particle is ≈ 4 Gev/c2).


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