The neutral deuterium atom, ${}^{2}_{1}$ H,has a mass of 2.014102 u; a neutral ordinary 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 deuterium nucleus? (1 u = 931.5 MeV/c²)

Question

Quizplus · Accepted Answer

The mass of a deuterium nucleus (${}^{2}_{1}$H) is given as 2.014102 u. This is more than the sum of the masses of a proton and a neutron, which is 1.007277 u + 1.008665 u = 2.015942 u. The difference between these two masses is called the mass defect (Δm) and represents the amount of mass converted to energy during the formation of the nucleus.

Δm = (sum of the masses of individual nucleons) - (mass of the nucleus)

Δm = (1.007277 u + 1.008665 u) - 2.014102 u = 0.00184 u

The binding energy (BE) of the nucleus can be calculated using Einstein's famous equation E=mc², where E is the energy, m is the mass, and c is the speed of light.

BE = Δmc²

BE = 0.00184 u × 931.5 MeV/u = 1.7146 MeV ≈ 2.2 MeV

Therefore, the binding energy of the deuterium nucleus is approximately 2.2 MeV. The correct answer is (C).

The Neutral Deuterium Atom 12{}^{2}_{1}12​ H,has a Mass of 2

The Neutral Deuterium Atom ${}^{2}_{1}$ H,has a Mass of 2