We may assume that a gold nucleus has a radius of 6.98 fm, and an particle has a radius of 1.8 fm. We have to find the energy the particle must have to touch the gold nucleus.

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The atomic number of gold is 79. Therefore, the charge of a nucleus is . It is given that we may use for the radius of gold nucleus 6.98 fm and for the radius of particle 1.8 fm. When the particle just touches the nucleus the separation between their centres will be

.

The energy that the particle must have to touch the gold nucleus will therefore be equal to the potential energy of the particle and the gold nucleus when the separation of their centres is . We have