Nuclear binding energy: The neutral deuterium atom, H, 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 H nucleus? (1 u = 931.494 MeV/c²)

Question

Quizplus · Accepted Answer

We can calculate the mass defect of the 11eb6b7b_2f34_a207_b0cf_dd20e9618c41_TB8274_11 H nucleus as follows:

Mass of protons = 2 × 1.007277 u = 2.014554 u
Mass of neutrons = 1 × 1.008665 u = 1.008665 u
Mass of 11eb6b7b_2f34_a207_b0cf_dd20e9618c41_TB8274_11 H nucleus = 2.014102 u

Mass defect = (2.014554 + 1.008665) - 2.014102 = 0.008117 u

The binding energy can be calculated using Einstein's famous equation, E=mc²:

Binding energy = 0.008117 u × 931.494 MeV/c² = 7.565 MeV

Therefore, the binding energy of the 11eb6b7b_2f34_a207_b0cf_dd20e9618c41_TB8274_11 H nucleus is 7.565 MeV. However, we are asked for the binding energy per nucleon, so we divide by the number of nucleons in the nucleus:

Binding energy per nucleon = 7.565 MeV / 2 = 3.7825 MeV

Therefore, the best choice is C, 2.2 MeV, because it is the closest choice to 3.7825 MeV.

Nuclear Binding Energy: the Neutral Deuterium Atom, H, Has