Find the binding energy per nucleon (in MeV/nucleon) 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

Quizplus · Accepted Answer

The binding energy of a nucleus is given by the formula

BE = [Z(Mp) + (A-Z)(Mn) - M]c^2

where BE is the binding energy, Z is the atomic number, A is the mass number, Mp is the mass of a proton, Mn is the mass of a neutron, M is the mass of the nucleus, and c is the speed of light.

Using the given data, we can calculate the mass of carbon-12:

M = 12u x (1.66 x 10^-27 kg/u) = 1.99 x 10^-25 kg

We can also calculate the number of protons and neutrons in carbon-12:

Z = 6
A-Z = 6

Next, we can calculate the total mass of the protons and neutrons in carbon-12:

Z(Mp) + (A-Z)(Mn) = 6(1.007825u) + 6(1.008665u) = 12.09888u

Substituting these values into the binding energy formula, we get:

BE = [6(1.007825u) + 6(1.008665u) - 12.000000u]c^2 = 92.162 MeV

The binding energy per nucleon is then:

BE/A = 92.162 MeV/12 = 7.68 MeV/nucleon

Rounding to the nearest tenth gives a final answer of 7.7 MeV/nucleon, which corresponds to choice D.

Find the Binding Energy Per Nucleon (In MeV/nucleon) of Carbon-12