Physics

Physics

Problem

Given the following data: • Mass of proton =1.007276 u=1.007276\,\text{u} • Mass of neutron =1.008665 u=1.008665\,\text{u} • Mass of deuteron (12H^{2}_{1}\text{H}) =2.013553 u=2.013553\,\text{u} • Mass of helium-4 nucleus (24He^{4}_{2}\text{He}) =4.002603 u=4.002603\,\text{u} (Take 1 u=931.5 MeV ⁣/c21\,\text{u}=931.5\,\text{MeV}\!/c^{2}.) a. (a) Determine the mass defect of the deuteron in atomic mass units. b. (b) Calculate the binding energy per nucleon of the deuteron in MeV. c. (c) Calculate the binding energy per nucleon of the helium-4 nucleus and state which of the two nuclei is more stable on this basis.
Intuitive explanation

This problem is about mass defect and binding energy—the idea that a nucleus weighs less than the sum of its separate nucleons because energy is released when they bind together. Calculate how much mass is "missing" by comparing the actual nucleus mass to what the individual protons and neutrons would weigh alone, then convert that tiny mass difference into energy using Einstein's E=mc2E=mc^2. This energy difference reveals how tightly the nucleus is held together.

Intuitive explanation

This problem is about mass defect and binding energy—the idea that a nucleus weighs less than the sum of its separate nucleons because energy is released when they bind together. Calculate how much mass is "missing" by comparing the actual nucleus mass to what the individual protons and neutrons would weigh alone, then convert that tiny mass difference into energy using Einstein's E=mc2E=mc^2. This energy difference reveals how tightly the nucleus is held together.

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