Explain the nuclear binding energy with example 16 8 O

Dear Student, We know that the nucleus is made up of protons and neutrons. So, logically, the mass of the nucleus = the sum of masses of the protons and neutrons, right? Not really! The nuclear mass (M) is always less than this sum. To e=understand this better, let’s look at an example, 16 8 O has 8 protons and 8 neutrons. Now, Mass of 8 neutrons = 8 × 1.00866 u Mass of 8 protons = 8 × 1.00727 u Mass of 8 electrons = 8 × 0.00055 u Therefore the expected mass of 168O nucleus = = 8 × 2.01593 u = 16.12744 u. We know from mass spectroscopy experiments that the atomic mass of 16 8 O is 15.99493u. Subtracting the mass of 8 electrons from this, we get the experimental mass of 16 8 O nucleus = 15.99053u (15.99493u – [8 x 0.00055u]). Hence, we see that there is a difference between the two numbers of 0.13691u (16.12744 u – 15.99053u). In simple words, the mass of the 16 8 O nucleus is less than the total mass of its constituents by 0.13691u. This difference in mass of a nucleus and its constituents is called the mass defect (ΔM) and is given by ΔM = [Zmp + (A – Z)mn] – M … (2) So, what exactly does mass defect mean? The mass of an oxygen nucleus < the sum of masses of its protons and neutrons (in an unbounded state). Therefore, the equivalent energy of the oxygen nucleus < the sum of the equivalent energies of its constituents. We can also say that if you want to break down an oxygen nucleus into 8 protons and 8 neutrons, then you must provide the extra energy (ΔMc^2). The relation between this energy (Eb) to the mass defect (ΔM) is derived from Einstein’s mass-energy equivalence relation {equation (1)}. Therefore, Eb = ΔMc^2… (3) In other words, if certain protons and neutrons are brought together to form a nucleus of a certain charge and mass, then an energy Eb is released in the process. This energy is called the Binding Energy of the nucleus. So, if we want to separate a nucleus into protons and neutrons, then we will need to provide an energy Eb to the particles. Regards