Physics · nuclei · NEET
When nucleons bind, energy is released to the outside. By E = mc^2, releasing energy means the system loses mass. So the bound nucleus is lighter than its free, separate nucleons. The missing mass equals the energy given out during binding. Example: an oxygen-16 nucleus is lighter than its 8 protons plus 8 neutrons by 0.13691 u (NCERT value).
For any stable nucleus the mass defect Delta M is always POSITIVE, because the nucleus mass is always smaller than the total mass of its free nucleons. We take Delta M = (mass of free nucleons) minus (mass of nucleus), so the answer comes out positive. A negative value would mean the nucleus is heavier than its parts, which does not happen for bound nuclei.
Mass defect is the missing MASS (measured in u or kg). Binding energy is the ENERGY equal to that missing mass, found using E = (Delta M)c^2. They describe the same thing in two units: multiply the mass defect by 931.5 to convert u into MeV. Mass defect is the cause; binding energy is its energy value.
Strictly, mass defect uses the NUCLEAR mass (no electrons). But in numericals we are usually given ATOMIC masses. If you use atomic mass of the nuclide, you must also use the mass of a hydrogen ATOM (m_H) for each proton instead of m_p, so the electron masses cancel. Read the question: if masses are 'atomic', pair them with m_H; if 'nuclear', use m_p.
Use 1 u = 931.5 MeV/c^2. So binding energy in MeV = Delta M (in u) times 931.5. For example, if Delta M = 0.0304 u, then energy = 0.0304 x 931.5 = about 28.3 MeV. This is the standard NEET shortcut, faster than using kilograms and 3x10^8 m/s.
Four statements are given below (A is the mass number): A. The volume of a nucleus is proportional to A^(1/3). B. The volume of a nucleus is proportional to A. C. The difference in mass of an atom and its nucleus is called the mass defect. D. The difference in mass of a nucleus and its constituents is called the mass defect. Choose the correct answer.
Delta M = Z*mp + (A-Z)*mn - M, where Z is the number of protons, A is the mass number, (A-Z) is the number of neutrons, mp and mn are proton and neutron masses, and M is the actual nucleus mass.
From NCERT: mass of a proton mp = 1.00727 u and mass of a neutron mn = 1.00866 u. Also 1 u = 931.5 MeV/c^2.
The oxygen-16 nucleus is lighter than its 8 protons and 8 neutrons by Delta M = 0.13691 u (NCERT). This corresponds to a large binding energy of about 127.5 MeV.
No, for any bound nucleus (except a single free nucleon, where there is nothing to bind) the mass defect is positive. A zero mass defect would mean no binding energy, so the nucleus would not stay together.
Mass defect leads directly to binding energy, binding energy per nucleon, nuclear stability, and the energy released in fission and fusion. It is the base concept for the whole Nuclei chapter.
