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Question

why approximately all the kinetic energy given to alpha particles in alpha decay ?

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Solution

In alpha decay, the nucleus emits an alpha particle; an alpha particle is essentially a helium nucleus, so it's a group of two protons and two neutrons. A helium nucleus is very stable
This reaction can be treated as a super-elastic collision between a light object (the alpha particle) and a relatively heavy particle (the remaining atom).

The kinetic energies of the two are:

alpha particle: 1/2mv2 = 1/2 (mv) * v

heavy atom: 1/2MV2 = 1/2 (MV) * V

To conserve momentum mv = MV, so v, the speed of the alpha particle afterwards, is larger than V, the speed of the heavy atom, by a factor of M/m. The kinetic energy of the alpha particle is also larger than that of the heavy atom by the same factor.

In other words, the alpha particle takes most of the kinetic energy.


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