Mass defect and binding energy Cambridge International AS & A Level Physics revision
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In plain words
Weigh a nucleus and you find something odd: it is lighter than the protons and neutrons it is made from. The missing mass was given out as energy when the nucleus formed. To pull the nucleus apart again you would have to pay that energy back, and that amount is its binding energy.
5 things to know
- Mass and energy are equivalent: E = mc². A change in mass Δm goes with a change in energy ΔE = c²Δm.
- Mass defect: the difference between the total mass of the separate protons and neutrons and the mass of the nucleus they make.
- Binding energy: the energy needed to separate a nucleus completely into its individual protons and neutrons. It equals the mass defect × c².
- Masses are given in atomic mass units: 1 u = 1.66 × 10⁻²⁷ kg. Energies are given in MeV: 1 MeV = 1.60 × 10⁻¹³ J.
- Binding energy per nucleon is the binding energy divided by the nucleon number. The bigger it is, the more stable the nucleus. It is greatest for nuclei near iron-56.
Worked example
A helium-4 nucleus has a mass of 4.0015 u. A proton has a mass of 1.0073 u and a neutron 1.0087 u. Find the binding energy of helium-4.
- Mass of two protons and two neutrons = 2 × 1.0073 + 2 × 1.0087 = 4.0320 u.
- Mass defect = 4.0320 − 4.0015 = 0.0305 u = 0.0305 × 1.66 × 10⁻²⁷ = 5.06 × 10⁻²⁹ kg.
- Binding energy = c²Δm = (3.00 × 10⁸)² × 5.06 × 10⁻²⁹ = 4.6 × 10⁻¹² J, which is about 28 MeV.
Tips and tricks
- Keep every decimal place in the masses. A mass defect is a small difference between two large numbers, and rounding early destroys it.
- Binding energy is not energy the nucleus has. It is energy that would have to be supplied to take the nucleus apart.
It lands in your notebook with its questions as flashcards.
Mass defect and binding energy: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
How does the mass of a nucleus compare with the total mass of its separate protons and neutrons?
The difference is the mass defect.
What is the binding energy of a nucleus?
It is the energy equivalent of the mass defect.
Which of these nuclei has the greatest binding energy per nucleon?
The curve peaks near iron.
How much energy is equivalent to a mass of 1.0 kg?
E = mc².
What does a greater binding energy per nucleon mean?
More energy is needed, for each nucleon, to take it apart.
Quiz
5 questions
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Worksheet
4 questions, 9 marks. Write your answers on paper, then check them.
Mass defect and binding energy
Cambridge International AS & A Level Physics 9702 · 9 marks · papermunch.org
Name ______________________________ Date ______________
State what is meant by mass defect and by binding energy.[2]
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Mass defect is the difference between the total mass of the separate nucleons and the mass of the nucleus. Binding energy is the energy needed to separate the nucleus completely into its individual nucleons.
A nucleus has a mass defect of 0.50 u. Find its binding energy in joules.[2]
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7.5 × 10⁻¹¹ J. 0.50 × 1.66 × 10⁻²⁷ × (3.00 × 10⁸)².
Helium-4 has a binding energy of 28.4 MeV. Find its binding energy per nucleon.[2]
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7.1 MeV per nucleon.
The Sun radiates energy at a rate of 3.8 × 10²⁶ W. Find the mass it loses each second.[3]
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4.2 × 10⁹ kg. 3.8 × 10²⁶ ÷ (3.00 × 10⁸)².
Answers: Mass defect and binding energy
- 1. Mass defect is the difference between the total mass of the separate nucleons and the mass of the nucleus. Binding energy is the energy needed to separate the nucleus completely into its individual nucleons.
- 2. 7.5 × 10⁻¹¹ J. 0.50 × 1.66 × 10⁻²⁷ × (3.00 × 10⁸)².
- 3. 7.1 MeV per nucleon.
- 4. 4.2 × 10⁹ kg. 3.8 × 10²⁶ ÷ (3.00 × 10⁸)².