Consider the decay of a free neutron at rest: n → p + e. Show that the two-body decay of this type must necessarily give an electron of fixed energy and, the therefore, cannot account in the observed continuous energy distribution in the β-decay of a neutron or a nucleus (Fig.)

Consider the decay of a free neutron at rest: n → p + e. Show that

1.	Consider the decay of a free neutron at rest: n → p + e. Show that the two-body decay of this type must necessarily give an electron of fixed energy and, the therefore, cannot account in the observed continuous energy distribution in the β-decay of a neutron or a nucleus (Fig.)
Answer» If the decay of neutron (inside the nucleus) into proton and electron is according to the given scheme, then the available energy in the decay must be carried out by the electron coming out of the nucleus and therefore the emitted electron should always possess a fixed value of K.E. However, the graph shows that the emitted electron can have any value of energy between zero and maximum value. Therefore, the given decay mode cannot account for the abserved continuous energy spectrum in the β-decay.