Consider the beta decay of an unstable `._(6)^(14)C` nuleus initially at rest: `._(6)^(14)C rarr ._(7)^(14)N +._(-1)^(0)e +v._(e)`.
Is it possible for the maximum kinetic energy of the emiited beta particle to be exactly equal to `Q`?

Explanation

In beta decay, total energy and momnetum is conserved. The loss of mass shows up as the gain of kinetic energy of the product particles. As there is initially no momnetum, there should be no total. Momentum after the decay. Even if the daughter nucleus does not recoil, the neutrino must move in a direction exactly oppsotite that of the beta particle to preserve zero momentum. Hence, the beta particle cannot get all of `Q` as its kinetic energy. Some amount must go to either the neutrino or the daughter nucleus(or to both) to cancel the momentum of the beta particle. Thus, for the beta particle, `K_(max) l e Q`.