A nucleus undergoes fission and breaks up into two middle-mass fragments, and . We have to answer the following: (a) By what percentage the does the surface are of the nucleus change during the process? (a) By what percentage does its volume change? (c) By what percentage does its electrostatic potential energy change? The electrostatic potential energy of a uniformly charged sphere of radius r and charge Q is given by

Solution:             Click For PDF Version

We will calculate the radii of and nuclides using the empirical relation

The radius of the nucleus will therefore be

The radius of the nuclide will be

And, the radius of the nuclide will be

The atomic number of nuclide is 92, that of nuclide is 54, and the atomic number of nuclide is 38. Therefore, the charge contained in a nucleus is 92e, the charge contained in a nucleus is 54e, and the charge contained in a nucleus is 38e.

(a)

The surface area of the nucleus will therefore be

The total surface area of one nucleus and one nucleus will be

The percentage change in the area of the nucleus when it fissions into one nucleus of and one nucleus of will therefore be

(b)

The volume of the nucleus will therefore be

The total volume of one nucleus and one nucleus will be

And, the percentage change in the volume of the nucleus when it fissions into one nucleus of and one nucleus of will therefore be

(c)

The electrostatic potential energy of a uniformly charged sphere of radius r and charge Q is given by

The electrostatic potential energy of a nucleus will be

The total electrostatic potential energy of one nucleus and one nucleus will be

The percentage change in the potential energy of the nucleus when it fissions into one nucleus of and one nucleus of will therefore be