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Energy of emitted alpha particle

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Calculate the energy released in the alpha decay of Po-210. Calculate the energy of the alpha particle.

Solution Summary

I explain how to take recoil effects into account to calculate the energy of the alpha particle.

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We can find the masses of the isotopes from various online resources (e.g. Wikipedia has a list of the properties of isotopes of all elements). The masses are:

Po-210: 209.9828737 u

Pb-206: 205.9744653 u

He-4: 4.00260325415 u

Here u is the atomic mass unit:

1 u = 1.66053904*10^(-27) kg

and the isotope masses refer to the atomic masses, this thus includes the electrons and the binding energy of the electrons.

When Po-210 decays by emitting an alpha particle (i.e. a He-4 nucleus), we end up with a fast moving He-4 nucleus and a doubly ionized Pb-206 atom. If we ignore the change in the binding energy due to re-arranging the electrons, then we can also shift two electrons from the doubly ionized Pb-206 to the He-4 and simply ...

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