Answer to Question #189297 in Chemistry for Udit Kumar

Question #189297

What is the binding energy (in kj/mol nucleon) for Indium-113, which has a mass of 112.90430 g/mol?


1
Expert's answer
2021-05-05T07:12:09-0400

Solution:

The energy equivalent of the mass defect is called the binding energy (Eb).


Step 1. Calculate the mass defect

The mass defect can be calculated as

Δm = Σ(mass of nuclear particles) - (mass of isotope)


The number of protons = atomic number = 49

The mass number for indium-113 = 113

The number of neutrons = mass number - atomic number = 113 - 49 = 64

113In → 49 1H + 64 1n


The atomic mass of indium-113 (113In) = 112.90430 g/mol

The 1H mass = 1.00783 g/mol

The neutron (n) mass = 1.00867 g/mol


Hence, for one mole of indium-113:

Δm = [(49 mol 1H)(1.00783 g/mol 1H) + (64 mol n)(1.00867 g/mol n)] - (1 mol 113In)(112.90430 g/mol 113In) = 1.03425 g = 1.03425×10-3 kg


Step 2. Calculate energy equivalent of the mass defect.

ΔE = (Δm)c2 (units: J = kg m2 s-2)

ΔE = (1.03425×10-3 kg) × (2.998×108 m/s)2 = 9.2958×1013 J = 9.2958×1010 kJ


Step 3. Divide the binding energy by the number of moles of nucleons (mass number) to get the binding energy per mole nucleons.

Eb = (9.2958×1010 kJ) / (113 mol nucleons) = 8.2264×108 kJ/mol nucleons

Eb = 8.2264×108 kJ/mol nucleons


Answer: The binding energy for Indium-113 is 8.2264×108 kJ/mol nucleons.

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