Question

Determine the binding energy per nucleon of an Mg-24 nucleus. The Mg-24 nucleus has a mass of 24.30506. A proton has a mass of 1.00728 amu, a neutron has a mass of 1.008665 amu, and 1 amu is equivalent to 931 MeV of energy.

Group of answer choices

4.41 MeV

8.83 MeV

0.113 MeV

106 MeV

0.3050 MeV

Answer 1

number of proton = 12
mass of each proton = 1.00728
so, total mass of proton,
mp = 12 * 1.00728
mp = 12.08736 amu

number of neutron = 12
mass of each neutron = 1.008665
so, total mass of neutron,
mn = 12 * 1.008665
mn = 12.10398 amu
Expected mass of nucleus = mass of protons + mass of neutrons
= 12.08736 + 12.10398
= 24.19134 amu

Actual mass of nucleus = (24.30506 - sum of mass of electrons)
Actual mass of nucleus = (24.30506 - 12* mass of 1 electron)
Actual mass of nucleus = (24.30506 - 12* 5.5E-4)
Actual mass of nucleus = 24.19134 amu

So, mass defect,
Δm = total mass of proton and neutron - actual mass of nucleus
Δm = 24.19134 - 24.19134
Δm = -0.10712 amu
This difference in mass need to be converted to binding energy

Since 1 atomic mass unit = 931.5 MeV
so,
E = -0.1071 * 931.5 MeV
= -99.78 MeV


m(dm)= -0.10712 amu

Since 1 u = 1.6605E-27 Kg
So,
dm = -0.1071/1.6605E-27
= -6.451*10^25 amu
Since 1 atomic mass unit = 931.5 MeV
so,
E = -6.451*10^25 * 931.5 MeV
= -6.009*10^28 MeV
This is energy of 1 atom

Number of nucleon in 1 atom= 24
So,
Energy per nucleon = energy of 1 atom / Number of nucleo
= -4.158/24 MeV/nucleon
= -4.16 MeV/nucleon

4.41 MeV IS CLOSEST
Answer: 4.41 MeV