Using the given information, calculate the mass defect of \( {}^{16}_{8}\mathrm{O} \) nucleus in \( \mathrm{MeV/c^2} \).
mass of electron, \( m_e = 0.00055\,\mathrm{u} \)
mass of proton, \( m_p = 1.00727\,\mathrm{u} \)
mass of neutron, \( m_n = 1.00866\,\mathrm{u} \)
experimental mass of nucleus = 15.99053 u
\( 1\,\mathrm{u} = 931.5\,\mathrm{MeV/c^2} \) (where u = atomic mass unit)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 127.5\,\mathrm{MeV/c^2} \)
The mass defect is the difference between the total mass of the separate nucleons and the mass of the nucleus. \( {}^{16}_{8}\mathrm{O} \) has 8 protons and \( 16 - 8 = 8 \) neutrons.
\( \displaystyle \Delta m = Z\,m_p + (A - Z)\,m_n - M_{\mathrm{nucleus}} \)
The given mass is the mass of the nucleus, so it is compared with the bare protons and neutrons; the electron mass is not needed.
\( \displaystyle Z\,m_p + (A - Z)\,m_n = 8 \times 1.00727\,\mathrm{u} + 8 \times 1.00866\,\mathrm{u} = 16.12744\,\mathrm{u} \)
\( \displaystyle \Delta m = 16.12744\,\mathrm{u} - 15.99053\,\mathrm{u} = 0.13691\,\mathrm{u} \)
\( \displaystyle \Delta m = 0.13691 \times 931.5\,\mathrm{MeV/c^2} \approx 127.5\,\mathrm{MeV/c^2} \)
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Nuclear Binding Energy – “… Therefore the expected mass of \( {}^{16}_{8}\mathrm{O} \) nucleus = 8 × 2.01593 u = 16.12744 u. … Substracting the mass of 8 electrons (8 × 0.00055 u) from this, we get the experimental mass of \( {}^{16}_{8}\mathrm{O} \) nucleus to be 15.99053 u. Thus, we find that the mass of the \( {}^{16}_{8}\mathrm{O} \) nucleus is less than the total mass of its constituents by 0.13691u. The difference in mass of a nucleus and its constituents, ΔM, is called the mass defect, and is given by
\( \displaystyle \Delta M = [Z m_p + (A - Z) m_n] - M \qquad (13.7) \)”
Nuclear Binding Energy – “… Example 13.3 Find the energy equivalent of one atomic mass unit, first in Joules and then in MeV. Using this, express the mass defect of \( {}^{16}_{8}\mathrm{O} \) in MeV/c2. … For
\( \displaystyle {}^{16}_{8}\mathrm{O},\ \Delta M = 0.13691\,\mathrm{u} = 0.13691 \times 931.5\,\mathrm{MeV/c^2} = 127.5\,\mathrm{MeV/c^2} \)”