Question

If the mass of the nucleus of carbon-12 is 12u and carbon-14 is 14.003 u, mass of proton is 1.001 u, and mass of neutron is 1.004 u then
find the binding energy of C-12 and C-14 nucleus
also find the binding energy of C-12 and C-14 nucleus per nucleon
the answer should be accurate to 4 decimal places

Answer 1

Answer:

The more tightly bound a system is, the stronger the forces that hold it together and the greater the energy required to pull it apart. We can therefore learn about nuclear forces by examining how tightly bound the nuclei are. We define the binding energy (BE) of a nucleus to be the energy required to completely disassemble it into separate protons and neutrons. We can determine the BE of a nucleus from its rest mass. The two are connected through Einstein’s famous relationship E = (Δm)c2. A bound system has a smaller mass than its separate constituents; the more tightly the nucleons are bound together, the smaller the mass of the nucleus.

Imagine pulling a nuclide apart as illustrated in Figure 1. Work done to overcome the nuclear forces holding the nucleus together puts energy into the system. By definition, the energy input equals the binding energy BE. The pieces are at rest when separated, and so the energy put into them increases their total rest mass compared with what it was when they were glued together as a nucleus. That mass increase is thus Δm = BE/c2. This difference in mass is known as mass defect. It implies that the mass of the nucleus is less than the sum of the masses of its constituent protons and neutrons. A nuclide AX has Z protons and N neutrons, so that the difference in mass is ∆m = (Zmp