Overview
This lecture explains how nuclei are described using atomic number and mass number, discusses isotopes, and covers how to calculate atomic mass using isotopic abundances.
Describing the Nucleus
- Nuclei are described by atomic number (Z, number of protons) and mass number (A, protons + neutrons).
- The atomic number determines the element’s identity and is found on the periodic table.
- The mass number is not listed on the periodic table and must be provided or calculated.
- Atoms of the same element always have the same number of protons but may have different numbers of neutrons (isotopes).
Atomic Number, Mass Number, and Isotopes
- Atomic number (Z) = number of protons; determines element type.
- For a neutral atom, number of protons = number of electrons.
- Isotopes are atoms of the same element with different mass numbers due to varying neutrons.
- Mass number (A) = number of protons + number of neutrons.
- Neutron count = mass number − atomic number.
Isotope Notation and Calculations
- Isotope names are written as Element-Mass Number (e.g., carbon-12, uranium-235).
- Isotope symbols use the element symbol with the mass number as a superscript (e.g., ¹⁴N).
- To find neutrons: subtract atomic number from mass number.
Practice Examples
- Phosphorus-31: 15 protons, 15 electrons, 16 neutrons (31–15).
- Uranium-235: 92 protons, 92 electrons, 143 neutrons (235–92).
- Chromium isotope with 24 protons and 28 neutrons: mass number 52, written as chromium-52 (⁵²Cr).
Atomic Weight and Its Calculation
- The atomic weight (bottom number on the periodic table) is the weighted average of all naturally occurring isotopes.
- Atomic weight calculation: sum of (fractional abundance × isotope mass) for all isotopes.
- Fractional abundance = percent abundance divided by 100.
Example Atomic Weight Calculations
- For carbon: atomic weight = (natural abundance of carbon-12 × mass) + (abundance of carbon-13 × mass), etc.
- For bromine: calculate using abundances (converted to fractions) and isotope masses, limit significant figures to most precise value provided.
- For boron: if one isotope’s percent abundance is given, the other is 100% minus that value.
Key Terms & Definitions
- Atomic Number (Z) — Number of protons in an atom’s nucleus; defines the element.
- Mass Number (A) — Total of protons and neutrons in the nucleus.
- Isotope — Atoms of the same element with different numbers of neutrons.
- Atomic Weight — Weighted average mass of all naturally occurring isotopes of an element.
- Fractional Abundance — The fraction (not percent) of a particular isotope in a natural sample.
Action Items / Next Steps
- Practice identifying atomic and mass numbers, and calculating numbers of protons, neutrons, and electrons for given isotopes.
- Try sample atomic weight calculations using provided isotope abundances and masses.
- Review periodic table information for element identification based on atomic number.