Read the following passage and answer the questions.
The oxygen nucleus \({}^{16}_{8}\mathrm{O}\) contains 8 protons and 8 neutrons. A student adds up the masses of 8 free protons and 8 free neutrons. She then compares this total with the mass of the oxygen nucleus. The mass of the oxygen atom is measured very precisely with a mass spectrometer, and the mass of the nucleus is found from it. The nucleus turns out to be lighter than its separate nucleons put together. This difference in mass is called the mass defect. The nucleons stay together in the nucleus because of the nuclear force. The student also looks at a graph of the binding energy per nucleon against the mass number A for a large number of nuclei. The curve is smooth and changes slowly. At nuclides such as \({}^{4}\mathrm{He}\) and \({}^{16}\mathrm{O}\), it shows small peaks.
A mass spectrometer gives the atomic mass of \({}^{16}_{8}\mathrm{O}\) as 15.99493 u. To find the mass of its nucleus from this value, one must
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → subtract the mass of 8 electrons
A mass spectrometer measures the mass of the whole atom. A neutral oxygen atom has 8 electrons outside its nucleus, one for each proton. So the atomic mass is the nuclear mass plus the mass of these 8 electrons. Each electron has a mass of 0.00055 u.
\( \begin{aligned} M_{\text{nucleus}} &= M_{\text{atom}}-8m_e \\ &= 15.99493-8\times0.00055 \\ &= 15.99493-0.00440 \\ &= 15.99053\ \mathrm{u} \end{aligned} \)
Option (1) add the mass of 8 electrons — Incorrect. The electron masses are already included in the atomic mass. Adding them would count them twice.
Option (2) subtract the mass of 8 protons — Incorrect. The protons are inside the nucleus, so their mass is part of the nuclear mass.
Option (3) subtract the mass of 8 electrons — Correct. Removing the 8 electron masses from the atomic mass leaves the mass of the nucleus alone, 15.99053 u.
Option (4) subtract the mass of 16 electrons — Incorrect. The number of electrons equals the atomic number, 8. The number 16 is the mass number, which counts nucleons.
NCERT (2026-27):
Nuclear binding energy – “The atomic mass of 168O found from mass spectroscopy experiments is seen to be 15.99493 u. Substracting the mass of 8 electrons (8 × 0.00055 u) from this, we get the experimental mass of 168O nucleus to be 15.99053 u.”