Binding Energy per Nucleon Graph (Edexcel International A Level Physics)

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Ann H

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Ann H

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Binding Energy per Nucleon Graph

  • When comparing the stability of different nuclei, it is useful to look at the binding energy per nucleon
  • The binding energy per nucleon is defined as:

The binding energy of a nucleus divided by the number of nucleons in the nucleus

  • A higher binding energy per nucleon indicates a higher stability since it requires more energy to pull the nucleus apart

  • Iron (A = 56) has the highest binding energy per nucleon, which makes it the most stable of all the elements

Binding Energy per Nucleon

By plotting a graph of binding energy per nucleon against nucleon number, the stability of elements can be inferred

Key Features of the Graph

  • At low values of A:
    • Nuclei tend to have a lower binding energy per nucleon, hence, they are generally less stable
    • This means the lightest elements have weaker electrostatic forces and are the most likely to undergo fusion

  • Helium (4He), carbon (12C) and oxygen (16O) do not fit the trend
    • Helium-4 is a particularly stable nucleus hence it has a high binding energy per nucleon
    • Carbon-12 and oxygen-16 can be considered to be three and four helium nuclei, respectively, bound together

  • At high values of A:
    • The general binding energy per nucleon is high and gradually decreases with A
    • This means the heaviest elements are the most unstable and likely to undergo fission

Worked example

Determine the binding energy per nucleon of Iron-56 (F presubscript 26 presuperscript 56 e) in MeV

Mass of a neutron = 1.675 × 10−27 kg

Mass of a proton = 1.673 × 10−27 kg

Mass of a F presubscript 26 presuperscript 56 e nucleus = 9.288 × 10−26 kg

Step 1: Calculate the mass defect

Number of protons, Z = 26

Number of neutrons, A – Z = 56 – 26 = 30

Mass defect, Δm = Zmp + (A – Z)mn – mtotal

Δm = (26 × 1.673 × 10-27) + (30 × 1.675 × 10-27) – (9.288 × 10-26)

Δm = 8.680 × 10-28 kg

Step 2: Calculate the binding energy of the nucleus

Binding energy, ΔE = Δmc2

E = (8.680 × 10-28) × (3.00 × 108)2 = 7.812 × 10-11 J

Step 3: Calculate the binding energy per nucleon

Binding energy per nucleon = E over A

E over H equals fraction numerator 7.812 space cross times space 10 to the power of negative 11 end exponent over denominator 56 end fraction space equals space 1.395 space cross times space 10 to the power of negative 12 end exponent space J

Step 4: Convert to MeV

J → eV: divide by 1.6 × 10-19

eV → MeV: divide by 106

binding energy per nucleon = fraction numerator 1.395 space cross times space 10 to the power of negative 12 end exponent over denominator 1.6 space cross times space 10 to the power of negative 19 end exponent end fraction space equals space 8 space 718 space 750 space e V space equals space 8.7 space M e V space left parenthesis 2 space s. f right parenthesis

Exam Tip

Checklist on what to include (and what not to include) in an exam question asking you to draw a graph of binding energy per nucleon against nucleon number:

  • You will be expected to draw the best fit curve AND a cross to show the anomaly that is Helium
  • Do not begin your curve at A = 0, this is not a nucleus!
  • Make sure to correctly label both axes AND units for binding energy per nucleon
  • You will be expected to include numbers on the axes, mainly at the peak to show the position of iron (56Fe)

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Ann H

Author: Ann H

Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students no matter their schooling or background.

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