Find the binding energy (in MeV) of carbon-12.Assume: mC = 12.000000 u
M p = 1.007825 u
M n = 1.008665 u
U = 1.66 *10-27 kg
A)14.8
B)0.511
C)9.11
D)92.3
E)46.2

Question

Quizplus · Accepted Answer

The binding energy (BE) can be calculated using the formula:

BE = [Z(mass of proton) + (A-Z)(mass of neutron) - mass of nucleus]c^2

Where Z is the atomic number, A is the mass number, and c is the speed of light.

For carbon-12, Z=6 and A=12. Substituting the given values, we get:

BE = [6(1.007825 u) + 6(1.008665 u) - 12.000000 u]c^2 
   = (6.018150 u - 12.000000 u) c^2 
   = (-5.981850 u) c^2

Converting u to kg, we get:

BE = (-5.981850 u)(1.66 x 10^-27 kg/u) c^2 
   = (-9.93076 x 10^-10 kg) c^2

Finally, converting kg to MeV using E=mc^2, we get:

BE = (-9.93076 x 10^-10 kg) (2.998 x 10^8 m/s)^2 / (1.602 x 10^-13 MeV) 
   = 92.3 MeV

Therefore, the correct answer is D) 92.3.

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