Question

The isotope Cobalt-60 has a nuclear mass of 59.933820 u
Calculate the Mass Defect of Cobalt-60 using the following information.
Mass of Proton: 1.007825 u
Mass of Neutron: 1.008665 u
1 u = 931.5 MeV

Answer 1

The mass defect is the difference between the sum of the masses of the constituents of the nucleus(nucleons) and the actual mass of the atom.

Mass of nucleons = Z*m_p + (A-Z)*m_n

Z - atomic number or number of protons/electrons

A - atomic mass

(A-Z) - Number of neutrons

m_p - mass of proton

m_n - mass of neutron

Mass defect, $\Delta$ m = Mass of nucleons - calculated mass

   $\Delta$ m = [Z*m_p + (A-Z)*m_n] - Calculated mass

In our question, we have to find the mass defect of cobalt, ₂₇Co⁶⁰ with Z= 27 and A=60

m_p = 1.007825 u

m_n = 1.008665 u

Now to plug in all the terms,

Mass defect, $\Delta$ m = [Z*m_p + (A-Z)*m_n] - 59.933820

= [27*1.007825 + (60-27)*1.008665] - 59.933820

= [27.211275 + 33.285945] - 59.933820

= 60.49722 - 59.933820

= 0.5634 u

In eV, the mass defect = 0.5634 * 931.5 MeV

= 524.8071 MeV

To remember:

• $\Delta$ m = [Z*m_p + (A-Z)*m_n] - Calculated mass

These are a couple of conversion formulae that you'll fund useful:

• 1u = 931.5 MeV
• 1u = 1.66054e-27 kg