Chemistry Fundamentals: Atomic Mass and Isotopes

The Unified Atomic Mass Unit ($u$)

• Definition and Value:

  • The unified atomic mass unit is a standard unit used to measure mass on an extremely small scale, such as the mass of atoms or subatomic particles.

  • It is defined exactly as: $1.66054027 \times 10^{-27}\,kg$.

  • To visualize the scale of this number, it would be written as a decimal point followed by 26 zeros and then the sequence 1660540 ($0.00000000000000000000000000166054027\,kg$).

  • This number is described as "unimaginably small" and can primarily be abstracted through mathematics.

• Rationale for the Unit:

  • The unit was defined this way to make the calculation of atomic and subatomic masses "cleaner."

  • Roughly speaking, the mass of a proton is approximately $1$ unified atomic mass unit ($u$).

  • Roughly speaking, the mass of a neutron is approximately $1$ unified atomic mass unit ($u$).

Masses of Subatomic Particles

• Protons:

  • The precise mass of a proton is approximately $1.007\,u$.

• Neutrons:

  • The mass of a neutron is slightly larger than that of a proton, approximately $1.008\,u$.

• Electrons:

  • The mass of an electron is significantly smaller than that of a proton or neutron.

  • An electron's mass is approximately $\frac{1}{2000}$ (two-thousandth) the mass of a proton or neutron.

• Atomic Mass Composition:

  • An atom consists of protons, neutrons (usually), and electrons.

  • Because electrons have such a negligible mass compared to nucleons, the mass of an atom is concentrated almost entirely in the nucleus (the protons and neutrons).

  • Knowing the total number of protons and neutrons in a nucleus provides a very good estimation of its atomic mass.

The Periodic Table and Element Identity

• Element Abbreviations:

  • Elements are represented by abbreviations (e.g., $H$ represents Hydrogen).

• Atomic Number:

  • The number located at the top of an element's cell on the periodic table is the atomic number.

  • The atomic number defines the identity of an element by specifying exactly how many protons are in its nucleus.

  • Specific Examples:

    • Any atom with exactly $1$ proton is defined as Hydrogen.

    • Any atom with exactly $20$ protons is defined as Calcium ($Ca$).

    • Any atom with exactly $36$ protons is defined as Krypton ($Kr$).

Isotopes and the Case of Hydrogen

• Isotopes Defined:

  • Isotopes are different versions of a given element.

  • They all share the same number of protons (defining them as that element) but have different numbers of neutrons.

• Hydrogen Isotopes:

  • Roughly $99.98\%$ of the hydrogen in the universe consists of atoms with exactly $1$ proton and $0$ neutrons.

  • Versions of hydrogen with $1$ or $2$ neutrons also exist, though they are much less common.

  • A neutral hydrogen atom (the most common version) contains $1$ proton, $0$ neutrons, and $1$ electron.

• Mass of Hydrogen Isotopes:

  • The mass of the most common hydrogen isotope is essentially the mass of a proton plus an electron.

  • Due to the electron's small size, the mass is approximately $1\,u$.

  • More precisely, adding the mass of a proton and an electron yields a value closer to $1.008\,u$, which is reflected on the periodic table.

Understanding Atomic Weights and Averages

• Weighted Average Mass:

  • The value listed on the periodic table for phosphorus or hydrogen is not the mass of a single atom. It is a weighted average of the various isotopes of that element found in nature.

  • It aligns closely with the most common isotope because that isotope represents the vast majority of the observed element.

• Hypothetical Weighted Average Calculation Example:

  • If an element has two isotopes:

    • Isotope 1: $80\%$ abundance with a mass of $5\,u$.

    • Isotope 2: $20\%$ abundance with a mass of $6\,u$.

  • The weighted average is calculated as: $(0.80 \times 5) + (0.20 \times 6) = 4.0 + 1.2 = 5.2\,u$.

• Terminology and Nuance:

  • Average Atomic Mass: The proper term for the weighted average of isotopic masses.

  • Atomic Weight: An older term used in chemistry books. This is technically inaccurate because the value describes mass, not weight.

  • Relative Atomic Mass: When values on the periodic table are written without the unit ($u$), they are unitless. This expresses how heavy an atom is relative to others.

    • Example: Carbon has a relative atomic mass of approximately $12$, meaning a carbon atom is roughly $12$ times heavier than the average hydrogen atom (which is approx $1$).

    • If units ($u$) were added, the relative atomic mass of Oxygen ($16$) would be expressed as an average atomic mass of $16\,u$.