Question

(a) How much energy is required to separate the typical middle-mass nucleus 120Sn into its constituent nucleons?

(b) What is the binding energy per nucleon for this nuclide?

Answer 1

Answer:

(a) We can find this energy from Q = Δmc2. Following standard particle, we carry out such calculations in terms of the masses of the neutral atoms involved, not those of the bare nuclei. Each hydrogen atom has a mass of 1.007825 u, and each neutron a mass of 1.008665 u. The combined mass of the constituent particle is  

m = (50×1.007825 u) + (70×1.008665 u)

  = 120.997 80 u

This exceeds the atomic mass of 120Sn by  

Δm = 120.99780 u – 119.902 199 u

     = 1.095601 u  

    ≈ 1.096 u

Q = Δmc2

  = (1.096 u) (931.5 MeV/u)

  = 1021 MeV

Therefore, the energy is required to separate the typical middle-mass nucleus 120Sn into its constituent nucleons would be 1021 MeV.

(b) The total binding energy Q is the total energy that must be supplied to dismantle the nucleus. The binding energy per nucleon En is then

En = Q/A = 1021 MeV/120 = 8.51 MeV/nucleon

From the above observation we conclude that, the binding energy per nucleon for this nuclide would be 8.51 MeV/nucleon.