Why are a significant number of beta particles found to have an energy smaller than the maximum?
remember that beta particles are electrons and are much smaller than an atom. So, when they travel, they pass "through" the atoms coming closer the the highly positive nucleus. This causes electrostatic interaction and slows down the beta particle. This is one of the many possible cases. If you elaborate the question, we can provide a more concerned reason.
ELECTROKID, The reason that in beta decay the beta particle has a distribution of energies is that the decay final state involve three particles carrying the energy and momentum. In this situation the total energy of the final state is divided among the three particles i.e., the new nucleus, the beta particle and the neutrino. From classical mechanics you know that the energy can be divided among them in an infinite combination.
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