An atom of 113I has a mass of 112.923650 amu. Calculate the binding energy in MeV per NUCLEON. Enter your answer with 3 significant figures and no units.

Question

Use the masses: mass of 1H atom = 1.007825 amu

mass of a neutron = 1.008665 amu

1 amu = 931.5 MeV

Answer 1

Nuclear binding energy is the energy required to break down a nucleus into its component nucleons (protons and neutrons).

Iodine, or I-113, has 113 as the mass number (sum of protons +neutrons)

Since iodine has an atomic number of 53, the # of protons is 53.

# of neutrons = mass number- # of protons = 113-53 = 60 neutrons.

Calculation of the nuclear binding energy involves determining the Mass Defect (difference between the actual mass of a nucleus and the sum of the masses of the nucleons of which it is composed)

To calculate mass defect:

1. add up the masses of each proton and of each neutron that make up the nucleus,
2. subtract the actual mass of the nucleus from the combined mass of the components to obtain the mass defect.

Combined mass = 53 protons (1.007825 amu) + 60 neutrons (1.008665 amu) = 113.934625 amu

Mass defect = combined mass-actual mass = 113.934625-112.923650 = -1.010975 amu

Convert answer from amu to MeV: -1.010975 amu (931.5 MeV/1amu) = about 942 MeV

Since the # of nucleons is the mass number, or 113 in this case, we will get the answer in the unit of MeV/nucleon by doing 942 MeV/113 nucleons.

After the calculation with 3 significant figures, we should get -8.33 MeV/nucleon.