Set out the steps for finding the binding energy per nucleon of a nucleus from its measured mass.

Count the protons and neutrons, add their separate masses, subtract the measured nuclear mass to get the mass defect, multiply that by 931.5 to get the binding energy in MeV, then divide by the nucleon number. Working in u throughout keeps the numbers manageable.

How many protons and neutrons does a nucleus of ⁷₃Li contain?

It contains 3 protons and 4 neutrons. Subtracting the proton number 3 from the nucleon number 7 leaves the neutron count.

Calculate the mass defect of ⁷₃Li, taking the proton mass as 1.00728 u, the neutron mass as 1.00867 u and the nuclear mass as 7.01436 u.

The separated nucleons total 3 × 1.00728 + 4 × 1.00867 = 3.02184 + 4.03468 = 7.05652 u. Subtracting the nuclear mass gives a mass defect of 7.05652 − 7.01436 = 0.04216 u.

A lithium-7 nucleus has a mass defect of 0.04216 u. Calculate its binding energy per nucleon.

The binding energy is 0.04216 × 931.5 = 39.3 MeV, so the binding energy per nucleon is 39.3/7 = 5.61 MeV. Multiplying 5.61 MeV by 7 and dividing by 931.5 MeV u⁻¹ returns a mass defect of 0.0422 u.

Convert a binding energy of 39.3 MeV into joules.

The binding energy is 39.3 × 1.60 × 10⁻¹³ = 6.29 × 10⁻¹² J. Dividing 6.29 × 10⁻¹² J by 1.60 × 10⁻¹³ J MeV⁻¹ returns 39.3 MeV.

Convert a mass defect of 0.03039 u into kilograms.

The mass defect is 0.03039 × 1.66 × 10⁻²⁷ = 5.04 × 10⁻²⁹ kg. Dividing 5.04 × 10⁻²⁹ kg by 1.66 × 10⁻²⁷ kg u⁻¹ returns 0.0304 u.

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Nuclear Energy

Calculating binding energy per nucleon

1 thing to know
Component 3

Overview

Recall questions on finding the mass defect from the constituent masses, converting it to an energy with E = Δmc², dividing by the nucleon number, the unified atomic mass unit and its energy equivalent, and worked determinations for named nuclides.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

How is a nuclear mass obtained from a quoted atomic mass?

Questions from this subtopic

Each one with the model answer underneath.

1
Set out the steps for finding the binding energy per nucleon of a nucleus from its measured mass.
Model answer
Count the protons and neutrons, add their separate masses, subtract the measured nuclear mass to get the mass defect, multiply that by 931.5 to get the binding energy in MeV, then divide by the nucleon number. Working in u throughout keeps the numbers manageable.
2
How many protons and neutrons does a nucleus of ⁷₃Li contain?
Model answer
It contains 3 protons and 4 neutrons. Subtracting the proton number 3 from the nucleon number 7 leaves the neutron count.
3
Calculate the mass defect of ⁷₃Li, taking the proton mass as 1.00728 u, the neutron mass as 1.00867 u and the nuclear mass as 7.01436 u.
Model answer
The separated nucleons total 3 × 1.00728 + 4 × 1.00867 = 3.02184 + 4.03468 = 7.05652 u. Subtracting the nuclear mass gives a mass defect of 7.05652 − 7.01436 = 0.04216 u.
4
A lithium-7 nucleus has a mass defect of 0.04216 u. Calculate its binding energy per nucleon.
Model answer
The binding energy is 0.04216 × 931.5 = 39.3 MeV, so the binding energy per nucleon is 39.3/7 = 5.61 MeV. Multiplying 5.61 MeV by 7 and dividing by 931.5 MeV u⁻¹ returns a mass defect of 0.0422 u.
5
Convert a binding energy of 39.3 MeV into joules.
Model answer
The binding energy is 39.3 × 1.60 × 10⁻¹³ = 6.29 × 10⁻¹² J. Dividing 6.29 × 10⁻¹² J by 1.60 × 10⁻¹³ J MeV⁻¹ returns 39.3 MeV.
6
Convert a mass defect of 0.03039 u into kilograms.
Model answer
The mass defect is 0.03039 × 1.66 × 10⁻²⁷ = 5.04 × 10⁻²⁹ kg. Dividing 5.04 × 10⁻²⁹ kg by 1.66 × 10⁻²⁷ kg u⁻¹ returns 0.0304 u.

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