Binding energy and nuclear stability

Overview

Recall questions on binding energy and mass defect, why a nucleus has less mass than its nucleons, the unified atomic mass unit and its energy equivalent, the mass defect, binding energy and binding energy per nucleon of helium-4, the binding energy curve and its peak near iron-56, fusion and fission from the curve, nucleon number, proton number and isotopes, and negative binding energy.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Define the binding energy of a nucleus.

   Model answer

   Binding energy is the energy that must be supplied to separate a nucleus completely into its individual protons and neutrons.

2. 2

   What is meant by the mass defect of a nucleus?

   Model answer

   The mass defect is the amount by which the mass of a nucleus is less than the total mass of the separate nucleons that make it up.

3. 3

   Why is the mass of a nucleus less than the sum of the masses of its nucleons?

   Model answer

   Energy is released when the nucleons come together, and since energy and mass are equivalent through Erest = mc², the bound system has correspondingly less mass.

4. 4

   State the value of the unified atomic mass unit in kilograms.

   Model answer

   One unified atomic mass unit is 1.661 × 10⁻²⁷ kg.

5. 5

   Calculate the energy equivalent of one unified atomic mass unit, in MeV.

   Model answer

   E = mc² = 1.661 × 10⁻²⁷ × (3.00 × 10⁸)² = 1.49 × 10⁻¹⁰ J, which is about 934 MeV.

6. 6

   The masses of a proton and a neutron are 1.0073 u and 1.0087 u, and the mass of a helium-4 nucleus is 4.0015 u. Calculate the mass defect.

   Model answer

   The separate nucleons total 2 × 1.0073 + 2 × 1.0087 = 4.0320 u, so the mass defect is 4.0320 − 4.0015 = 0.0305 u.

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