CHM111 Lecture 6: Comprehensive Study Notes on Binding Energy and Mass Defect

Binding Energy and Mass Defect

• Definition of Binding Energy

  • The energy that results from the difference in mass between the combined mass of protons and neutrons and the actual mass of the nucleus.

  • Nucleus consists solely of protons and neutrons, and thus, the expected mass equals the sum of the individual masses of protons and neutrons.

  • Weight of the nucleus (mass of nucleus) is less than the sum of its components, indicating energy is associated with that difference.

• Mass Defect

  • Refers to the difference in mass (mass defect) that gives rise to the binding energy of the nucleus.

  • Simplified Concept: The mass defect leads directly to the binding energy via the mass-energy equivalence formula:
    $\Delta E = \Delta m c^2$

  • Where:

    • $\Delta E$ = Change in energy

    • $\Delta m$ = Change in mass (mass defect)

    • $c$ = Speed of light (approximately $3 imes 10^8$ m/s)

Calculating Binding Energy

• Procedure for Calculation

  1. Convert mass of nickel-60 from atomic mass units (AMU) to kilograms.

  2. Ensure all energy calculations end in Joules, as SI units are required thus converting from AMU is essential because there is no direct energy unit in AMU.

  3. Obtain the net mass of the nucleus by subtracting the mass of electrons from the total mass of the atom.

  • Mass of nucleus = Mass of atom - Mass of electrons

  1. Calculate the mass of nucleons (protons and neutrons) where care must be taken because the number of neutrons differs from the number of protons.

  • Example: For nickel-60, determine neutrons where:

    • Number of Neutrons = Mass Number - Number of Protons = 60 - 28 (for nickel)

  1. Use the mass defect in the binding energy calculation: $\Delta E = \Delta m c^2$

  2. Converting the energy from Joules to kilojoules or joules per mole to contextualize the energy value.

  • Example: Energy available from 60 grams of nickel can produce binding energy.

• Energy Values

  • Example binding energy calculation yielded a value of: $8.46285 \times 10^{-11}$ Joules.

  • This can be represented per atom for clearer understanding.

  • Binding energy per mole can be expressed as kilojoules per mole using Avogadro's number, yielding values like $5.09633 \times 10^{10}$ kilojoules per mole, indicating significant energy implications.

Practical Implications of Binding Energy

• Harvesting Energy

  • If energy extraction from binding energy was done, it would destabilize the atom, as the extraction needs breaking the nucleus apart.

  • Process illustrated in nuclear reactors or hydrogen and atomic bomb designs, showcasing energy release through nuclear fission or fusion.

• Mass Predictions

  • When predicting mass related to energy, 1 AMU represents approximately 1 gram per mole, thus demonstrating that condensed quantities of material can yield large energy outputs.

• Important Concepts in Fusion and Fission

  • Fusion and fission both result in energy however, differ in how they operate between combining nuclei versus splitting them respectively.

General Remarks on Energy Measurements

• Understanding Scale of Energy Values

  • The values highlighted seem small (like typically 20 kilojoules for H-bonds), however the scale can mislead; binding energies (in context) equal considerable energy available from relatively small amounts of mass.

  • Encouragement given to represent binding energy in recognized units (e.g., per mole, kilojoules) facilitates understanding of scale.

• Conversion Efficiency

  • Efficiency in calculations maintained through appropriate unit measures; the stepwise approach ensures clarity in energy calculations involved in nuclear chemistry.