Question

I need those ASAP please!!!

(20 Marks) (a) Starting with the SEMF, explicitly derive an equation for the mass of an atom th A nucleons and Z protons, ma(A,2), as a quadratic polynomial with respect to Z.

Answer 1

Semi Empirical mass formula is given by, M(Z, A) = A(M_n - a_v) + a_s A^2/3 + Z [(M_p - M_n) - ac/A^1/3 - a_a 4) + Z^2 [ac/A^1/3 + 4a_a/A] + a_a A plusminus delta (a) implies M(Z)A) = alpha A + beta Z + gamma Z^2 plusminus delta alpha = M_n - (a_v - a_a - a_s/A^1/3) beta = -4 a_0 - (M_n - M_p) gamma = (4 a_a/A + a_c/A^1/3) [a_c rightarrow coulomb term coefficient a_a rightarrow symmetric term coefficient a_s rightarrow surface term coefficient a_v rightarrow volume term coefficient delta rightarrow pairing energy plusminus delta = paring energy = + delta for odd Z and odd N = 0 for odd Z and even N or vice versa = -delta for even Z and even N (b) (partial differential M/partial differential Z)_Z = Z_min = beta + 2 gamma z_min = 0 implies Z_min = -beta/2 gamma \r\n For odd A, (delta = 0), mass M(Z_min, A) of the most stable isobar is given by M(Z_0, A) = alpha A - 2 gamma Z^2_min + gamma Z^2_min M(Z_min, n) = alpha A - gamma Z^2_min. . .