# Estimate of the Range of the Weak Nuclear Force

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By considering the energy-time uncertainty principle, estimate the range of the weak nuclear interaction at low energies. Compare this range to the size of a typical nucleon (for example, a proton) and therefore explain why the weak nuclear interaction between individual nucleons is Ã¢??weakÃ¢??. (Hint Ã¢?" the maximum speed of an interaction-carrying boson, like any particle, is the speed of light.)

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#### Solution Preview

According to the uncertainty principle, a virtual W or Z particle may form for a time given approximately by

dT = hbar / dE, where dE = ...

#### Solution Summary

We use Heisenberg's uncertainty principle along with the known masses of the W and Z particles to estimate the range of the weak nuclear force at low energies.

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