3. (a) N and C are known as mirror nuclei, nuclei with the same mass number A, but with different numbers of protons Z.

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3 A N And C Are Known As Mirror Nuclei Nuclei With The Same Mass Number A But With Different Numbers Of Protons Z 1 (149.46 KiB) Viewed 74 times

3. (a) N and C are known as mirror nuclei, nuclei with the same mass number A, but with different numbers of protons Z. For mirror nuclei it is found that once the effects of the Coulomb forces are accounted for, their binding energies are identical. What does this tell us about the nature of the nuclear force? (b) An estimate of the Binding energy B(Z, A) for a nucleus with atomic number 2 and mass number A is given by the semi-empirical mass formula: [2] B(Z, A) = 21A – 22A2/3 a32(Z - 1) 04(A - 2Z)? A1/3 +8(Z, A)az A-3/4 A = = [8] where a1...5 are positive constants, and 8(Z, A) = +1 for (Z, A) even, 8(Z, A) = -1 for (Z, A) odd, and 8(Z, A) = () otherwise. Explain the physical meaning of each of the first three terms in the semi-empirical mass formula and provide a physical explanation of both the functional dependence on (Z,A), and on the sign of each of these three terms. (c) Justify the functional form of the last term on the RHS of the semi-empirical mass formula, in terms of our empirical knowledge on the stability of nuclei. (d) Using the semi-empirical mass formula given above, and assuming A is odd, show that the atomic number 2 corresponding to the maximum binding energy for a given, fixed value, of the mass number A is given by [2] a3 4133 + 404 Z= 20部+”) a3 404 41/3 А [6] [2] (e) What is the significance of this value of Z?