Question

Calculate the mass defect and nuclear binding energy (in Joules per nucleon) for C-16, a radioactive isotope of carbon with an actual mass of 16.01470 amu. The subatomic particle masses are: e– = 0.00055 amu, p + = 1.0073 amu, n0 = 1.0086 amu and 1 amu = 1.6605 x10–27 kg.

Answer 1

number of proton = 6

mass of each proton = 1.007

so, total mass of proton,

mp = 6 * 1.007

mp = 6.042 amu

number of neutron = 10

mass of each neutron = 1.0086

so, total mass of neutron,

mn = 10 * 1.0086

mn = 10.086 amu

Expected mass of nucleus = mass of protons + mass of neutrons

= 6.042 + 10.086

= 16.128 amu

Actual mass of nucleus = (16.0147 - sum of mass of electrons)

Actual mass of nucleus = (16.0147 - 6* mass of 1 electron)

Actual mass of nucleus = (16.0147 - 6* 5.5E-4)

Actual mass of nucleus = 16.0114 amu

So, mass defect,

Δm = total mass of proton and neutron - actual mass of nucleus

Δm = 16.128 - 16.0114

Δm = 0.1166 amu

This difference in mass need to be converted to binding energy

dm = 0.1166 u

1 u = 1.6605E-27 Kg

So,

dm = 0.1166*1.6605E-27

= 1.936*10^-28 Kg

mass can be converted to energy as given by:

E = m*c^2

so,

E = 1.936*10^-28*(3*10^8)^2 J

E = 1.743*10^-11 J

Total Binding energy = 1.743*10^-11 J

Number of nucleon = 16

Binding energy per nucleon =1.743*10^-11 J / 16

= 1.09*10^-12 J/nucleon

Answer: 1.09*10^-12 J/nucleon