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Question : 30 of 30
Marks: +1, -0
Consider the decay of a free neutron at rest : n→p+e−n \rightarrow p + e^{-}
Show that the two-body decay of this type must necessarily give an electron of fixed energy and, therefore, cannot account for the observed continuous energy distribution to the β-decay of a neutron of a nucleus as shown in the figure.
Solution:  
In the decay process, n→p+en \rightarrow p + e
energy of electron is equal to (Δm)c2(\Delta m)c^{2}
where Δm = mass defect
= mass of neutron – mass of proton and electron;
which is fixed. Therefore, two body decay of this type cannot explain the observed continuousenergy distribution in the b-decay of a neutron or a nucleus.
Note : The simple result of this exercise was one among the several arguments advanced by W. Pauli to predict the existence of a third particle in the decay products of β-decay. The particle is known as neutrino. We now know that it is a particle of intrinsic spin 12\frac{1}{2} (like e−,pe^{-}, p or nn), but is neutral, and either massless or having an extremely small mass (compared to electron’s mass) and which interacts very weakly with matter.The correct decay process of neutron is n→p+e−+vn \rightarrow p + e^{-} + v].
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