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Calculating Binding Energy (OCR A Level Physics): Revision Note

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Katie M

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Calculating Binding Energy

  • Binding energy can be calculated using the equation:

ΔE = c2Δm

  • Where Δm is the mass defect of a nucleus

  • This can be calculated using:

    Δm = Zmp + (A – Z)mn – mtotal

    • Where:

      • Z = proton number

      • A = nucleon number

      • mp = mass of a proton (kg)

      • mn = mass of a neutron (kg)

      • mtotal = measured mass of the nucleus (kg)

Worked Example

WE - Binding energy per nucleon question image

Answer:

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 = c2Δm

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 Worked Example equation 1
Binding Energy per Nucleon Worked Example equation 2

Step 4: Convert to MeV

J → eV: divide by 1.6 × 10-19

eV → MeV: divide by 106

Binding Energy per Nucleon Worked Example equation 3

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    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.