IGNOU BPHET 141 2026 - From the semi-empirical mass formula, calculate the value of the atomi

Question

From the semi-empirical mass formula, calculate the value of the atomic number (Z) for the most stable nucleus at a given mass number A. Calculate Z₀ for $A = 90$ .

19 Jan 2026

Answer :

Word Count : 275

The semi-empirical mass formula for the binding energy (B(A,Z)) of a nucleus is: [ B(A,Z) = a_v A - a_s A^{2/3} - a_c \frac{Z^2}{A^{1/3}} - a_a \frac{(A-2Z)^2}{A} + \delta ] For the most stable nucleus at a given (A), (\frac{\partial B}{\partial Z} = 0). Ignoring the pairing term (\delta), we differentiate with respect to (Z): [ \frac{\partial B}{\partial Z} = - 2 a_c \frac{Z}{A^{1/3}} + 4 a_a \frac{A-2Z}{A} = 0 ] Multiply through by

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