Question

An atom of 105In has a mass of 104.914558 amu. Calculate the binding energy in MeV per NUCLEON. Enter your answer with 3 significant figures and no units. Use the masses:

mass of 1H atom = 1.007825 amu
mass of a neutron = 1.008665 amu
1 amu = 931.5 MeV

Answer 1

The binding energy per nucleon for an atom of 105In is calculated by determining the mass defect, converting it to energy using Einstein's mass-energy equivalence, and dividing by the number of nucleons.

Step-by-step explanation:

To calculate the binding energy per nucleon in MeV for an atom of 105In with a mass of 104.914558 amu, we must first identify the number of protons and neutrons in the nucleus. Indium-105 has 49 protons (since In is the element with atomic number 49), and subtracting this from the mass number 105 gives us 56 neutons. The mass of the protons is 49 x 1.007825 amu, and the mass of the neutrons is 56 x 1.008665 amu.

Next, we calculate the mass defect by subtracting the atomic mass of the 105In from the combined mass of the protons and neutrons. To convert the mass defect into energy, we multiply by 931.5 MeV/amu, according to Einstein’s mass-energy equivalence principle (E=mc2). Lastly, we divide this energy by the total number of nucleons (protons + neutrons) to find the binding energy per nucleon.

Answer 2

8.46

Step-by-step explanation:

Atomic number : It is defined as the number of electrons or number of protons present in a neutral atom.

Also, atomic number of I = 549

Thus, the number of protons = 49

Mass number is the number of the entities present in the nucleus which is the equal to the sum of the number of protons and electrons.

Mass number = Number of protons + Number of neutrons

105 = 49 + Number of neutrons

Number of neutrons = 56

Mass of neutron = 1.008665 amu

Mass of proton = 1.007825 amu

Calculated mass = Number of protons*Mass of proton + Number of neutrons*Mass of neutron

Thus,

Calculated mass = (49*1.007825 + 56*1.008665) amu = 105.868665 amu

Mass defect = Δm = |105.868665 - 104.914558| amu = 0.954107 amu

The conversion of amu to MeV is shown below as:-

1 amu = 931.5 MeV

So, Energy = 0.954107*931.5 MeV/atom = 888.750671 MeV/atom

Also, 1 atom has 105 nucleons (Protons+neutrons)

So, Energy = 888.750671 MeV/105nucleons = 8.46 MeV/nucleon

Answer:- 8.46