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Understanding Atomic Mass and Isotopes

Mar 21, 2025

Lecture on Atomic Mass and Isotopes

Key Definitions

  • Mass Number: Total number of protons and neutrons in an atom. Always an integer.
    • Example: Carbon-13 has a mass number of 13.
  • Atomic Mass: The weighted average of the masses of the isotopes of an element, typically found on the periodic table.
    • Example: Carbon has an atomic mass of 12.01.

Calculating Atomic Mass

  • Weighted Average Calculation:
    • Atomic mass is calculated by taking the sum of the product of each isotope's mass and its relative abundance.
    • Example Formula:
      • ( \Sigma (\text{abundance}{i} \times \text{mass}{i}) )
  • Example with Neon:
    • Neon has three isotopes: Neon-20, Neon-21, and Neon-22.
    • Abundances: Neon-20 (90.48%), Neon-21 (0.27%), Neon-22 (9.25%).
    • Atomic mass for Neon is calculated as the sum of each isotope's abundance times its mass.

Examples and Problems

Example Calculations:

  • Boron:

    • Isotopes: Boron-10 (19.9%, 10.013 amu) and Boron-11 (80.1%, 11.009 amu).
    • Calculated Atomic Mass: 10.81 amu.

  • Silver:

    • Isotopes: Silver-107 (51.84%, 106.9051 amu) and Silver-109 (48.16%, 108.9048 amu).
    • Calculated Atomic Mass: 107.87 amu.

  • Copper:

    • Copper-63 (69.17%, 62.9396 amu) and Copper-65 (30.83%, 64.9278 amu).
    • Calculated Atomic Mass: 63.55 amu.

Problem Solving Strategy:

  1. Convert percentage abundance to decimal form.
  2. Multiply each isotope's mass by its decimal abundance.
  3. Sum all the products to find the atomic mass.
  4. Verify the reasonableness of the result by checking if it falls within expected values between the isotopes' masses.

Critical Thinking and Validation

  • Importance of using critical thinking to check the reasonableness of results.
  • Encouraged to not blindly trust calculator outputs.
  • Methods to validate calculations through comparisons with known periodic table values.

Advanced Problem Examples:

  • Bromine:

    • Given average atomic mass and one isotope's abundance, solve for the unknown isotope's mass and abundance.

  • Lithium:

    • Given two isotopes and average atomic mass, solve for the unknown's abundance.

  • General Approach:

    • Use algebra to solve for unknowns when given partial data.
    • Understand that the sum of isotopes' abundances must equal 100%.

Summary

  • Understanding atomic mass requires knowledge of isotopic abundances and individual isotope masses.
  • Critical thinking and verification through practical examples are crucial for mastering the concept.

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