For a nucleus with mass number A and atomic number Z: A. The surface energy per nucleon is b(s) = -a₁A²ᐟ³. B. The Coulomb contribution to the binding energy is b(c) = -a₂Z(Z - 1)/A⁴ᐟ³. C. The volume energy is b(v) = a₃A. 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. Here a₁, a₂ and a₃ are constants. Choose the most appropriate answer from the options given below:
Options

Question

For a nucleus with mass number A and atomic number Z: A. The surface energy per nucleon is b(s) = -a₁A²ᐟ³. B. The Coulomb contribution to the binding energy is b(c) = -a₂Z(Z - 1)/A⁴ᐟ³. C. The volume energy is b(v) = a₃A. 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. Here a₁, a₂ and a₃ are constants. Choose the most appropriate answer from the options given below:

Options

G1 Physics · Accepted Answer

Use the semi-empirical mass formula: B = a(v)A − a(s)A²ᐟ³ − a(a)(A − 2Z)²/A − a(c)Z(Z − 1)/A¹ᐟ³ + δ(A,Z) Now examine the statements. A. If the statement is for surface energy per nucleon, the A-dependence should be proportional to A⁻¹ᐟ³, not A²ᐟ³. So A is false. B. The total Coulomb term varies as −a(c)Z(Z − 1)/A¹ᐟ³. Therefore the printed A⁴ᐟ³ dependence is not the total Coulomb contribution. So B is false. C. The volume term is proportional to A: B(volume) = a(v)A. So C is true. D. Surface cor…