Question

3. Consider the fission of a nucleus (A, Z) into two equal fragments (A/2, Z/2). Use the semi-empirical mass formula. (a) Find the Q-value of this process and the condition on Z2/A for instability. (b) For what values of A is fission possible for nuclei lying along the line of stability? Compare this result with reality and speculate about the origin of the difference, if any

Answer 1

Q = m(B,A) – 2M (ſete) Using semi Emperical moss formule, binding Blant avd - 054% -0, Mainon (432 and for daughter nuclei 266.16) = 200,- 2049,9% -20-4 -2014.-2) Q value = Equation - Equation & as 13 (1-2%) + ac aliping [- sta] Negrecting s term (pairing energy term) at is very small number. Q - As [-0-2005 +0-370 2C"/ Using Using as = 15 as= 13.0 dc = 0.60 2 = 4/2 [ -3.38 + 0.22 Z(z = 1) mer for above conversion to take place Q >O z (z-1)

Condition on for stability is 2 5 for symmetric fission of Nuclei lying along the line of stability or - 12 - => N = 12 % or A = (N+Z) = 2.27 A = 2. 27 on, 415 Z 15 X 2.2 z7 33 Nuclei with zy 3 Can Undergo luclear fission In real & situation Ec is the coulombie which will yeild Q& Ę. part of Binding Energy 2 24 8 which fits more with experimental dete This Q Value should not only be positive, But it has to overcome Culomb potential hend 2 52 (Ans)