Answer to Question #189297 in Chemistry for Udit Kumar

Question

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

Answer 1

Solution:

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

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.

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

E_b = 8.2264×10⁸ kJ/mol nucleons

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