Atomic Structure, Isotopes, and Atomic Mass - Study Notes
Elements, Compounds, and Reactions
Elements are substances composed of only one kind of atoms. Each element is defined by atoms having the same number of protons (the atomic number, Z).
Compounds are types of matter composed of two or more different types of atoms chemically combined. For a compound, you must have at least two different kinds of atoms.
- Example: Water, H_2O, is formed from hydrogen and oxygen chemically combined.
Chemical reactions involve rearrangement of atoms, not creation or destruction of atoms. According to Dalton’s theory, atoms are rearranged to form new substances, but no atoms are created or destroyed.
Periodic table: There are currently 118 known elements. A few of the heaviest ones are radioactive and man-made; memorizing them is not essential for basic understanding.
Elements are denoted by chemical symbols, which can be:
- A single capital letter (e.g., H for hydrogen) or
- A capital letter followed by one or more lowercase letters (e.g., Na for sodium, Cl for chlorine).
Some symbols come from Latin names (e.g., gold is Au from aurum, silver is Ag from argentum, potassium from kalium). The symbol may not resemble the English name.
Notation basics: You should know the names and symbols of the common elements in the corner of your current table and a few by heart for quick recall. Do not write in the periodic table copy given to you in class.
Dalton’s contribution and laws:
- Law of conservation of mass: mass is conserved in chemical reactions; the total mass before equals the total mass after.
- Dalton’s atomic theory postulates: matter is composed of atoms which are indivisible in his time; atoms of a given element have the same properties; atoms combine in simple whole-number ratios to form compounds; chemical reactions involve rearrangement of atoms.
- The theory helped explain the law of multiple proportions: when elements form different compounds, the ratios of masses of one element that combine with a fixed mass of a second element are simple whole-number ratios.
Atomic structure fundamentals:
- Nucleus: small, dense, positively charged center containing protons and neutrons; most of the atom’s mass is in the nucleus.
- Electrons: negatively charged, very light particles that orbit the nucleus in regions around it; atoms are electrically neutral when the number of protons equals the number of electrons.
- Protons (p⁺): positively charged; mass similar to neutrons, much heavier than electrons.
- Neutrons (n⁰): electrically neutral; contribute to mass but not charge.
- Electrons (e⁻): negatively charged; mass ≈ 9.11 × 10⁻³¹ kg; charge ≈ −1.602 × 10⁻¹⁹ C.
Nuclear model and historical experiments:
- Rutherford’s gold foil experiment suggested a dense, positively charged nucleus because most alpha particles passed through but some were deflected or reflected, indicating a central concentrated mass.
- The nucleus contains protons (positive charge) and neutrons (no charge).
- The electron cloud surrounds the nucleus and balances the positive charge to yield a neutral atom.
Isotopes and isotopic notation:
- Isotopes are atoms of the same element (same Z) with different numbers of neutrons (different mass number A).
- Isotopes have the same atomic number Z but different mass numbers A = Z + N, where N is the number of neutrons.
- Isotopes can be denoted in two common ways:
- Nuclear notation: element symbol with Z in the lower-left corner and A in the upper-left corner (e.g., for sodium: {}^{A}_{Z} ext{X} or simply X-A).
- Example: Sodium-23 would be written as
- Nuclear notation: ^{23}_{11} ext{Na}
- Isotope name: Sodium-23.
- To find neutrons: N = A - Z.
- Common isotopes mentioned: Carbon has isotopes such as ^{12} ext{C}, ^{13} ext{C}, ^{14} ext{C}; Chlorine has isotopes ^{35} ext{Cl} and ^{37} ext{Cl}, etc.
Atomic number, mass number, and electron neutrality:
- The number of protons equals the atomic number Z and determines the identity of the element.
- In a neutral atom, the number of electrons equals the number of protons: ext{electrons} = Z.
- The mass number A = Z + N reflects total nucleons (protons + neutrons).
Atomic mass, atomic mass unit, and standard references:
- Atomic mass is the weighted average of the masses of all naturally occurring isotopes of an element.
- Unit of atomic mass: atomic mass unit (amu).
- 1 amu is defined as 1/12 of the mass of a carbon-12 atom: 1 ext{ amu} = rac{m( ext{C}^{12})}{12}.
- Numerically, 1 ext{ amu} ext{ is about } 1.660 imes 10^{-27} ext{ kg} (some texts use 1.6621 imes 10^{-27} ext{ kg} in teaching examples).
- Common practice: atomic masses shown on the periodic table are weighted averages of isotopes and are given in amu; carbon-12 is used as the standard reference for the scale.
- Mass of a single electron is tiny; the combined mass of many particles yields the element's atomic mass.
Mass spectrometry:
- Modern technique to determine relative atomic masses by measuring mass-to-charge ratios of ions in a mass spectrum.
Fractional abundance and calculating average atomic mass:
Naturally occurring isotopes have a fractional abundance (or percent abundance) that sums to 1 (or 100%).
To compute the average atomic mass of an element:
Convert percentage abundances to fractional abundances by dividing by 100.
Multiply each isotope mass by its fractional abundance and sum: ext{Average mass} =
\sumi fi \cdot m_i
Example: Chlorine has two main isotopes:
^{35} ext{Cl} with mass m1 = 34.968853 ext{ amu} and fractional abundance f1 \approx 0.7577
^{37} ext{Cl} with mass m2 = 36.965903 ext{ amu} and fractional abundance f2 \approx 0.2423
The average atomic mass of chlorine is approximately ext{avg} \approx f1 m1 + f2 m2 \approx 0.7577(34.968853) + 0.2423(36.965903) \approx 35.45 ext{ amu}
Notation for isotopes in calculations sometimes uses percentages; convert to fractions first, then perform the weighted sum.
Examples and short exercises referenced in class:
- Example: Potassium has Z = 19; for an isotope with A = 39, neutrons are N = A - Z = 39 - 19 = 20, giving the isotope notation ^{39}_{19} ext{K}.
- Example: Carbon-12 as a reference; note that for carbon-12, A = 12 and Z = 6, so N = A - Z = 6 neutrons for that isotope.
- Example: When asked to identify whether a given diagram represents a molecule, a pure element, or a compound, use the number of distinct atom types and their connections: a molecule may be two or more atoms bonded; a pure element is a single type of atom (e.g., O₂ is two oxygen atoms, a molecule but still a single element); a compound contains two or more different elements.
Quick summary keys for exam preparation:
- Atom = nucleus (protons, neutrons) + electrons around it; neutral atoms have equal numbers of protons and electrons.
- Atomic number Z = number of protons = number of electrons in a neutral atom.
- Mass number A = Z + N; neutron count N = A - Z.
- Isotopes: same Z, different A; notation can be X-A or ^{A}_{Z} ext{X}.
- Atomic mass is a weighted average over isotopes, measured in amu; 1 amu ≈ 1.6605 × 10⁻²⁷ kg (as a common reference).
- Fractional abundance: convert percentages to fractions by dividing by 100 before weighted averaging.
- Rutherford’s experiment and Dalton’s theory connect to how we understand mass conservation, nuclear structure, and chemical behavior.
Atomic Structure and Isotopes – Key Concepts in One Place
- Elements and compounds definitions
- Dalton’s theory and conservation of mass
- Periodic table basics: symbols, Z, and A concepts
- Electron discovery and mass/charge values
- Nuclear model: nucleus, protons, neutrons, electrons
- Isotopes and isotopic notation (Z and A)
- Atomic mass unit and standard (carbon-12)
- Mass spectrometry and average atomic mass calculation
- Practical isotope calculation example (chlorine) and a simple neutron calculation (potassium example)