Question

4.1. The nucleus of an atom is made up of protons and neutrons. Protons are charged positively. Coulomb's law mandates a force of repulsion between the protons. Predict why the nucleus does not blow itself apart? [5] 4.2. Explain what is meant by the following terms. (Your explanations should include appropriate mathematical equations as well): (i). Mass defect (ii). Binding energy (iii). Given the mass of a proton (1.6726 x 10-27 kg), mass of neutron (1.6749 x 10-27 kg) and the experimental mass of deuteron (3.3435 x 10-27 kg), determine (a) the mass defect and (b) the binding energy (in MeV) of deuteron H. ​

Answer 1

Step-by-step explanation:

The reason why the nucleus does not blow itself apart is because of the strong nuclear force. The strong nuclear force is stronger than the electrostatic repulsion between protons.

(i) Mass defect is the difference between the mass of an atom and the sum of the masses of its constituent particles.

(ii) Binding energy is the energy required to separate an atomic nucleus into its constituent nucleons.

(a) The mass defect of deuteron H is (mass of 1 proton + mass of 1 neutron) - mass of deuteron H = (1.6726 x 10^-27 kg + 1.6749 x 10^-27 kg) - 3.3435 x 10^-27 kg = 0.004 x 10^-27 kg.

(b) The binding energy of deuteron H is equal to the mass defect multiplied by the speed of light squared (c^2) divided by the Avogadro constant (NA) multiplied by 1 million (MeV conversion factor). Thus, the binding energy of deuteron H is (0.004 x 10^-27 kg) x (3 x 10^8 m/s)^2 / (6.022 x 10^23 mol^-1) x 10^6 = 2.224 MeV.