Question

Calculate the atomic mass of the silicon-30 nucleus in amu (to three decimal places) assuming that the mass of a nucleon is 1.008 amu and the binding energy per nucleon is 1.326×10⁻¹² J/nucleon. (1 kg = 6.022×10²⁶ amu)

Answer 1

The binding energy per nucleon for silicon-30 is 1.326*10^-12 J/nucleon

neucleons = protons + neutrons

                   = 14+16 = 30

Binding energy in J = 1.326*10^-12 *30 = 3.98*10^-11 J

   E = mC²

3.98*10^-11   =, m*(3*10⁸)²

m                 = 3.98*10^-11/9*10¹⁶

                    = 4.42*10^-28 Kg                       

                    = 4.42*10^-28 *6.022*10²⁶ amu                                     (1 kg = 6.022*10²⁶ amu)  

                      = 0.2661724 amu

mass diffect = 0.2661724amu

actual mass -theoreticl mass = mass diffect

(14*1.007825 + 16*1.008665 )-theoretical mass = 0.2661724

30.24819 -theoretical mass = 0.2661724

-Theoretical mass    = 0.2661724 -30.24819

    Theoretical mass of Si           = 29.9820176 amu

          Theoretical mass of Si           = 29.982 amu