Atomic Structure

1.1 Subatomic Particles

This section explains the basic components of atoms—protons, neutrons, and electrons—and how they determine atomic structure and chemical behavior.

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• Protons
  • Located in the nucleus; each has a mass of 1 atomic mass unit (amu)
  • Atomic number ($Z$) = number of protons
  • Mass number = protons + neutrons
• Isotopes have different mass numbers (same number of protons, different neutrons)
• Electrons
  • Mass ≈ 1/2000 that of a proton
  • Occupy electron shells; valence electrons are those in outermost shell
    • Involved in chemical bonding

1.2 Atomic Mass vs Atomic Weight

Differentiates between atomic mass (mass of a single atom) and atomic weight (average mass of isotopes weighted by abundance).

Khan Academy Video: Atomic number, mass number, and isotopes

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• Atomic Mass Unit (AMU)
  • Defined as 1/12 the mass of a carbon-12 atom
    • $1\ \text{amu} = 1.66 \times 10^{-24}\ \text{g}$
• Hydrogen Isotopes
  • Protium: 1 proton
  • Deuterium: 1 proton + 1 neutron
  • Tritium: 1 proton + 2 neutrons
  • Mass number implies that $6.022 \times 10^{23}$ atoms (1 mole) have a mass in grams equal to the atomic mass
• Atomic Weight
  • Weighted average of naturally occurring isotopes

1.3 Rutherford, Planck, and Bohr

Summarizes key models and discoveries explaining atomic structure and energy quantization, including Planck’s quantum theory and Bohr’s model of the hydrogen atom.

Khan Academy Video: Electronic structure: Bohr model through Absorption and emission

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• Planck’s Equation
  • $E = hf$
    • $h = 6.626 × 10^{-34} J·s$
    • (Planck’s constant)
    • $f$ = frequency
    • $E$ = energy of discrete quantum packets
• Bohr Model
• Angular Momentum: $L = mvr$ and $K = \frac{1}{2}mv^2$
• Restrictions on allowed values of $L$
• Quantized angular momentum: $L = \frac{nh}{2\pi}$
  • $n$ = principal quantum number
• Energy Levels: $E = -\frac{R_H}{n^2}$
  • $R_H = 2.18 \times 10^{-18}\ \text{J/electron}$ (Rydberg constant)
  • Energy increases as electron distance from nucleus ↑
• Ground State: $n = 1$
  • Lowest energy configuration
• Excited State: higher $n$ values
  • If returning to $n = 1$, the open shell is the s subshell
• Applications of Bohr Model
  • Atomic Emission Spectra
    • Energy emitted when electrons drop from excited → ground state
      • $E = \frac{hc}{\lambda}$
        • $c = 3.00 \times 10^8\ \text{m/s}$ (speed of light)
        • $\lambda$ = wavelength
  • Line Spectra
    • Each line corresponds to an electron transition
    • Used for analyzing starlight to determine elemental composition
  • Hydrogen Spectral Series
    • Lyman Series: transitions from $n > 2 \to n = 1$ (shorter wavelengths)
    • Balmer Series: $n > 3 \to n = 2$ (visible region; 4 main wavelengths)
    • Paschen Series: $n > 4 \to n = 3$
• Atomic Absorption Spectra
  • Each element has a unique spectrum
  • Reflects characteristic energy level structure

1.4 Quantum Mechanical Model of Atoms

Introduces the modern view of atomic structure based on probability distributions (orbitals) rather than fixed paths, and defines the quantum numbers that describe electron behavior.

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Khan Academy Video: Paramagnetism and diamagnetism

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• Electron Orbitals
  • Electrons move rapidly within localized regions around the nucleus
  • Position can only be expressed as a probability distribution
• Heisenberg Uncertainty Principle
  • Impossible to know both position and momentum of an electron simultaneously

• Quantum Numbers
  • Pauli Exclusion Principle: no two electrons can share the same 4 quantum numbers
  • 4 quantum numbers: $n, l, m_l, m_s$
  • Hund’s Rule: electrons fill each orbital singly (parallel spins) before pairing
• Principal Quantum Number (n)
  • Defines shell level (energy + radius)
  • Higher $n$ → higher energy + larger radius
  • Max electrons per shell: $2n^2$
  • Energy difference between shells: $\Delta E = \left(\frac{1}{n_i^2} - \frac{1}{n_f^2}\right)$
• Azimuthal Quantum Number (l)
  • Defines subshell shape (s, p, d, f)
  • Possible $l$ values: 0 → (n - 1)
  • Determines number of subshells in shell

    Subshell	Azimuthal Quantum # (l)	# of e⁻
    s	0	2
    p	1	6
    d	2	10
    f	3	14

  • Max electrons per subshell: $4l + 2$
• Magnetic Quantum Number (mₗ)
  • Specifies orbital orientation within a subshell
  • Range: $-l \leq m_l \leq l$
  • s = 1 orbital, p = 3, d = 5, f = 7
  • Determines magnetic properties
    • If $l = 0$, cannot have $m_l = \pm 1$ (since s only has one orbital)
• Spin Quantum Number (mₛ)
  • Two possible spins: +½ or −½
  • Electrons with same spin orientation = parallel spins
• Electron Configurations
  • Example: 2p⁴
  • Orbitals fill by increasing energy (e.g., 6s before 5d)
  • Hund’s rule: maximize unpaired spins
  • Paramagnetic: unpaired electrons
  • Diamagnetic: all electrons paired
  • When removing electrons, s orbitals empty before d
    • Example:
      • Zn: 3p⁶ 4s² 3d¹⁰
      • Zn²⁺: 3p⁶ 4s⁰ 3d¹⁰
• Valence Electrons
  • Outer (active) electrons in s and p subshells

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