For a nucleus X Z A having mass number A and atomic number Z A. The surface energy per nucleon ( b s ) = – a 1 A 2 3 . B. The Coulomb contribution to the binding energy b c = − a 2 Z ( Z − 1 ) A 4 3 .

Question

For a nucleus X Z A having mass number A and atomic number Z A. The surface energy per nucleon ( b s ) = – a 1 A 2 3 . B. The Coulomb contribution to the binding energy b c = − a 2 Z ( Z − 1 ) A 4 3 . C. The volume energy b v = a 3 A D. Decrease in the binding energy is proportional to surface area. E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( a 1 , a 2 and a 3 are constants) Choose the most appropriate answer from the options given below:

TestHub · Accepted Answer

The formula to calculate the radius of a nucleus is given by
$R = R_{0} A^{\frac{1}{3}} . . . (1)$
Hence, the volume energy can be written as
$\begin{array}{rcl} b_{v} & = & C_{1} R^{3} \\ = & a_{3} {(A^{\frac{1}{3}})}^{3} \\ = & a_{3} A \end{array}$
The nuclear binding energy is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons. Also, the energy of the nucleus is negative with regard to the energy of the particles pulled apart to infinite distance, because energy must be utilised to split a nucleus into its individual protons and neutrons. It is proportional to the surface area.
Hence, statements C and D are most appropriate.

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