Some of the heaviest atomic nuclei are radioactive and decay by emitting an part

Question

Some of the heaviest atomic nuclei are radioactive and decay by emitting an particle. These particles usually have a kinetic energy of about 5 MeV (depending on the type of nucleus) after they are far from the nucleus. Use this information to estimate the size of a nucleus by assuming that the particle leaves the edge of the nucleus with zero kinetic energy and that the electrostatic potential energy is the only potential energy it has at that position. Assume the charge on the nucleus is +88 e. The charge on an particle is +2e while the mass of an particle is 4.0026 amu where 1 amu = 1.66 x 10 -27 kg.

Explanation / Answer

Potential Energy of the alpha particle at the surface of the nucleus is 5 MeV P.E=9*10^9*88*4*e^2/R Where R is the approximate radius of the nucleus. P.E=5 MeV=5*10^6*e Joules equating we get R=9*10^9*88*4*e^2/(5*10^6*e)=9*10^9*88*4*1.6*10^(-19)/(5*10^6)=1.013*10^(-13) metres

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