Question

Calculate the nuclear binding energy in mega-electronvolts (MeV) per nucleon for 232Th if its nuclear mass is 232.038 amu.

Answer 1

The atomic mass of 232Th is 232.038 amu. Calculate the nuclear binding energy of this

nucleus and the corresponding nuclear binding energy per nucleon

Mass number = 232

No. of protons = 90, then

Neutrons = Mass number – proton number = 90protons and 232-90= 142 neutrons are present

Mass of proton = 1.007316

Mass of neutrón = 1.008665

Total mass = 90* 1.007316 + 142 *1.008665 = 233.88887amu

The mass defect:

232.038 -233.88887= -1.85087amu

Mass = 1.85087/(6.022*10^23) = 3.073*10^-24 g or -3.073*10^-27 kg

Energy released (Einstein E = mC^2)

E = m*C^2 = -3.073*10^-27 * (3*10^8)^2 = -2.7657*10^-10 J

Nuclear binding energy = E = -2.7657*10^-10 J

Nuclear binding energy per nucleon

Nucleon = neutron + protons = 232

E per nucleon = E / nucleon =( -2.7657*10^-10)/( 232) = 1.19211*10^-12 J/nucleon

1 J = 6.242e+12

Total MeV = (1.19211*10^-12)(6.242e+12) = 7.440 MeV