Atomic Structure, Isotopes, and Energy Levels - Quick Review chapter 4

Rutherford and Atomic Structure

  • Rutherford gold foil experiment: thin gold foil, alpha particle source, screen behind to detect dots. Observation: most alpha particles pass through; <1% deflected or reflected. Conclusion: atom is mostly empty space with a very small, dense, positively charged nucleus at the center; mass concentrated in the nucleus. This overturned Thomson’s plum pudding model.
  • Early models: Thomson's plum pudding (positively charged 'pudding' with embedded electrons) vs. Rutherford’s nuclear model (nucleus in center, electrons around outside).
  • Subatomic particles:
    • Proton, symbol: p (often p+), charge +1; mass ~ m_p \,\approx\, 1.007\text{ amu}
    • Neutron, symbol: n, charge 0; mass ~ m_n \,\approx\, 1.008\text{ amu}
    • Electron, symbol: e, charge -1; mass ~ m_e \approx 0.00055\text{ amu} (nearly zero compared to p and n)
  • Nucleus vs. electron cloud: nucleus contains protons and neutrons; electrons occupy the surrounding space in defined energy levels.
  • Size scales:
    • Nuclear diameter ~ d_{\text{nucleus}} \approx 10^{-15}\text{ m}
    • Atomic diameter ~ d_{\text{atom}} \approx 10^{-10}\text{ m}
    • Ratio: \frac{d{\text{nucleus}}}{d{\text{atom}}} \approx 10^{-5}
    • If nucleus ≈ 1 m, atom ≈ 10^5 m = 100 km (illustrates extreme emptiness of atom)
  • Atomic mass unit (AMU/Da):
    • Definition: 1\ \text{amu} = \frac{m(^{12}\text{C})}{12}
    • Carbon-12 has 6 protons and 6 neutrons; mass number A = Z + N; all isotopes of an element share Z but have different N.
  • Isotopes and atomic mass:
    • Isotopes: same element (same Z) with different neutron numbers (N) => different mass numbers (A).
    • Examples: Mg-24, Mg-25, Mg-26; C-12, C-13, C-14.
    • Atomic mass (as shown in periodic table) is the weighted average mass of all isotopes of the element.
    • Atomic mass units for protons/neutrons are about 1 amu; electrons are negligible in mass.
  • Isotopic notation and counting:
    • For an element X with Z protons and mass number A, the isotope is written as ^{A}_{Z}\mathrm{X} (A on top, Z on bottom).
    • Example: Lithium isotopes; the periodic-table average mass is close to the heavier isotope if it’s more abundant.
  • Atomic number and mass number:
    • Atomic number Z = number of protons = number of electrons in a neutral atom.
    • Mass number A = number of protons + number of neutrons = Z + N.
    • Knowing Z and A lets you determine p, n, and e counts:
    • Protons = Z
    • Neutrons = A - Z
    • Electrons = Z (in a neutral atom)
  • Ions vs. neutral atoms:
    • Ions: cation (positive) or anion (negative) due to loss or gain of electrons; in ions, electron count ≠ proton count.
  • Atomic mass in practice:
    • If element has isotopes i with masses Mi and abundances fi (as fractions), the average atomic mass is:
      \text{Atomic mass} = \sumi Mi fi = \sumi Mi \left(\frac{\%a0i}{100}\right)
    • Example: Mg has isotopes 24, 25, 26 with masses 23.99, 24.99, 25.98 amu and abundances 78.7%, 10.13%, 11.17%.
    • The commonly listed atomic mass on the periodic table is this weighted average, not a single isotope mass.
  • Example qualitative checks:
    • If the element’s average atomic mass is very close to a whole number, that isotope is dominant (e.g., Li-7 for lithium with average ~6.94 amu).
  • Electron energy levels and quantization:
    • Electrons occupy discrete energy levels outside the nucleus, not continuous space.
    • Principal energy levels: n = 1, 2, 3, 4, …; within each level there are sublevels (SPDF: s, p, d, f).
    • An electron can absorb exactly the right amount of energy (ΔE) to jump to a higher level; insufficient or excess energy does not cause a transition. This is quantum behavior.
    • Energy unit for level transitions: the electron-volt (eV).
    • When an electron returns from a higher level to a lower level, it emits energy as electromagnetic radiation; the spectrum spans gamma, X-ray, UV, visible, IR, microwave, and radio depending on ΔE.
  • Connection to the electromagnetic spectrum:
    • Higher frequency corresponds to higher energy photons (gamma > X-ray > UV > visible > IR > microwave > radio).
    • Visible light is only a small portion of the spectrum.
  • Energy-level organization terminology:
    • Main (principal) energy levels: n = 1, 2, 3, 4, …
    • Sublevels within each main level: SPDF (s, p, d, f);
    • Sublevels beyond f are not needed for elements currently in nature (as per course scope).
  • Summary takeaway:
    • Atoms are mostly empty; a tiny, dense nucleus contains protons and neutrons and carries most of the mass and positive charge.
    • Electrons are arranged in quantized energy levels; transitions lead to photon emission/absorption and define the atomic spectra.
    • Isotopes differ by neutrons; atomic mass is a weighted average reflecting isotopic abundances.
    • Atomic number Z fixes identity (element); mass number A fixes total nucleons; neutral atoms have equal numbers of protons and electrons.