Find the binding energy (in MeV) of carbon-12. Assume:
M_C = 12.000 000 u
M _p = 1.007 825 u
M _n = 1.008 665 u
U = 1.66 × 10−²⁷ kg

Question

Find the binding energy (in MeV) of carbon-12. Assume: M_C = 12.000 000 u M _p = 1.007 825 u M _n = 1.008 665 u U = 1.66 × 10−²⁷ kg A) 14.8 B) 0.511 C) 9.11 D) 92.3 E) 46.2

Quizplus · Accepted Answer

The binding energy of a nucleus can be calculated using the mass defect, which is the difference between the mass of the nucleus and the sum of the masses of its protons and neutrons. For carbon-12 ($^{12}C$), which has 6 protons and 6 neutrons:Mass of protons = $6 \times 1.007825 \, u = 6.04695 \, u$Mass of neutrons = $6 \times 1.008665 \, u = 6.05199 \, u$Total mass of protons and neutrons = $6.04695 \, u + 6.05199 \, u = 12.09894 \, u$Mass defect = $12.09894 \, u - 12.000000 \, u = 0.09894 \, u$To convert the mass defect into energy (MeV), we use Einstein's equation $E = mc^2$, where $m$ is the mass in kilograms, $c$ is the speed of light ($3.00 \times 10^8 \, m/s$), and $E$ is the energy in joules. However, in nuclear physics, it's common to use atomic mass units (u) and directly convert to MeV using the conversion factor $1 \, u = 931.5 \, MeV/c^2$:Binding energy = $0.09894 \, u \times 931.5 \, MeV/u = 92.16 \, MeV$Therefore, the closest answer is 92.3 MeV.

Find the Binding Energy (In MeV) of Carbon-12