The neutral deuterium atom, , has a mass of 2.014102 u; a neutral hydrogen atom has a mass of 1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u. What is the binding energy of the nucleus? 1 u = 931.494 MeV/c².

Question

Quizplus · Accepted Answer

The mass of the deuteron nucleus is 2.014102 u, but the combined mass of a proton and a neutron is 2.016942 u. This difference in mass is due to the binding energy of the nucleus, which is released when the nucleons come together to form the nucleus. We can calculate the binding energy using Einstein's famous equation, E=mc^2:

Δm = (2.016942 u - 2.014102 u) = 0.00284 u
E = Δmc^2 = (0.00284 u)(931.494 MeV/c^2/u) = 2.646 MeV

Therefore, the binding energy of the deuteron nucleus is 2.646 MeV, which is closest to choice C (2.2 MeV).

The Neutral Deuterium Atom, , Has a Mass of 2.014102