Atomic Structure, Electronic Configuration, and Atomic Models

Development of Atomic Models & Dalton's Atomic Theory

• Evolution of Atomic Theory: Atomic models evolved over time as new experimental evidence, observations, and scientific discoveries emerged.

• Dalton's Atomic Model (1808):

  • Proposed by John Dalton as the first scientific atomic theory.

  • Main Postulates:

  • All matter consists of tiny, indivisible, and indestructible units called atoms.

  • Atoms of the same element are identical in mass and chemical properties.

  • Atoms of different elements possess different masses and properties (e.g., $\text{Hydrogen} \neq \text{Carbon}$).

  • Compounds form when atoms combine in simple, whole-number ratios (e.g., $\text{H}_2\text{O}$ combines in a $2:1$ ratio).

  • Chemical reactions involve only the rearrangement of atoms; atoms are neither created nor destroyed.

  • Significance: Explained the Law of Conservation of Mass and the Law of Definite Proportions.

  • Limitations:

  • Atoms are divisible into subatomic particles ($\text{protons}$, $\text{neutrons}$, and $\text{electrons}$).

  • Atoms of the same element can differ in mass due to isotopes.

  • Atoms can be converted into energy in nuclear reactions.

Discovery of Subatomic Particles

• Discovery of the Electron (J.J. Thomson, 1897):

  • Observed cathode rays generated in gas discharge tubes under low pressure ($\approx 10^{-4}\,\text{atm}$).

  • Cathode rays originate from the negative cathode, travel toward the positive anode, possess mass (move paddle wheels), carry negative charge, and deflect in electric and magnetic fields.

  • Thomson determined the specific charge-to-mass ratio ($e/m_e$): $\frac{e}{m_e} = 1.758820 \times 10^{11}\,\text{C\,kg}^{-1}$

  • Millikan's Oil Drop Experiment (1909): Measured the elementary charge of an electron: $e = -1.6022 \times 10^{-19}\,\text{C}$

  • Calculated Mass of an Electron: $m_e = \frac{e}{e/m_e} = 9.1094 \times 10^{-31}\,\text{kg}$

• Discovery of the Proton (Goldstein, ~1886):

  • Used perforated cathode tubes to discover positive canal/anode rays traveling opposite to cathode rays.

  • For hydrogen gas, the positive particle (proton) properties are:

  • Charge: $+1.6022 \times 10^{-19}\,\text{C}$

  • Mass: $1.6726 \times 10^{-27}\,\text{kg}$ ($\approx 1836$ times heavier than an electron)

• Discovery of the Neutron (James Chadwick, 1932):

  • Bombarded beryllium with $\alpha$-particles, emitting uncharged radiation capable of knocking protons out of paraffin wax.

  • Neutral charge, mass $1.6750 \times 10^{-27}\,\text{kg} \approx 1\,\text{amu}$, located inside the nucleus.

Early Atomic Models & Limitations

• Thomson's Plum Pudding Model (1898):

  • Pictured the atom as a sphere of uniform positive charge with embedded electrons.

  • Failed to explain $\alpha$-particle scattering results and lacked a central nucleus or structured electron arrangement.

• Rutherford's Nuclear Model (1911):

  • Bombarded thin gold foil with $\text{He}^{2+}$ ($\alpha$-particles).

  • Observations: Most particles passed undeflected, a small fraction deflected at small angles, and very few reflected back sharply.

  • Conclusions:

  • The atom consists mostly of empty space.

  • Mass and positive charge are concentrated in a tiny central nucleus.

  • Electrons orbit the nucleus in circular paths.

  • Dimensions:

  • Atomic radius: $1 \times 10^{-10}\,\text{m}$

  • Nuclear radius: $1 \times 10^{-15}\,\text{m}$ (atom is $100,000$ times larger than the nucleus)

  • Atomic Parameters:

  • Atomic Number ($Z$): Number of protons in the nucleus.

  • Mass Number ($A$): Total number of protons and neutrons ($\text{nucleons}$): $A = Z + \text{number of neutrons}$.

  • Isobars: Species with identical mass number ($A$) but different atomic numbers ($Z$).

  • Isotopes: Species with identical atomic number ($Z$) but different mass numbers ($A$).

  • Drawbacks of Rutherford's Model:

  • Modeled Coulombic attraction between nucleus and electron analogous to gravitational orbits: $F = \frac{k q_1 q_2}{r^2}$.

  • According to Maxwell's electromagnetic theory, accelerating charged particles continuously emit radiation. An orbiting electron would continuously lose energy and collapse into the nucleus within $\approx 10^{-8}\,\text{s}$.

  • Could not account for discrete line spectra of atoms.

Electromagnetic Radiation & Light Theories

• Characteristics of Electromagnetic Radiation (EMR):

  • Consists of oscillating electric and magnetic fields perpendicular to each other and to the direction of wave travel.

  • All EMR travels at the speed of light in vacuum: $c = 3.0 \times 10^8\,\text{m/s}$

  • Wave equation relation: $c = \lambda \nu$

• Planck's Quantum Theory (1900):

  • Radiation is emitted or absorbed in discrete packets called quanta (or photons).

  • Energy of a quantum is directly proportional to frequency: $E = h \nu$

  • Planck's constant: $h = 6.626 \times 10^{-34}\,\text{J\,s}$

• Photoelectric Effect (Einstein, 1905):

  • Ejection of electrons from a metal surface when irradiated with light exceeding threshold frequency ($\nu_0$).

  • Photoelectric Equation: $\text{K.E.} = h \nu - W_0$

  • Key Relationships: Light intensity dictates the rate/number of ejected electrons; light frequency dictates the kinetic energy of emitted electrons.

• Wave-Particle Duality:

  • Wave phenomenon: Interference and Diffraction.

  • Particle phenomenon: Photoelectric effect and Blackbody radiation.

Atomic Spectra & Bohr's Atomic Model

• Atomic Line Spectra:

  • Excited atoms emit light at specific wavelengths, producing a line spectrum (atomic fingerprint) rather than a continuous spectrum.

  • Emission Spectrum: Bright lines on a dark background.

  • Absorption Spectrum: Dark lines on a continuous background.

  • Rydberg Formula for Hydrogen Balmer Series: $\frac{1}{\lambda} = R \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$

  • Rydberg constant: $R = 1.09678 \times 10^7\,\text{m}^{-1}$

  • Spectral Series:

  • Lyman Series: Transitions to $n_1 = 1$ (Ultraviolet region).

  • Balmer Series: Transitions to $n_1 = 2$ (Visible region).

  • Paschen Series: Transitions to $n_1 = 3$ (Infrared region).

• Bohr's Postulates (1913):

  • Stationary States: Electrons orbit the nucleus in non-radiating, fixed circular orbits.

  • Angular Momentum Quantization: $m_e v r = \frac{n h}{2 \pi}$

  • Energy Quantization: Energy absorption or emission occurs only during transitions between stationary states: $\Delta E = E_2 - E_1 = h \nu$

• Bohr Equations for One-Electron Species ($\text{H}, \text{He}^+, \text{Li}^{2+}, \text{Be}^{3+}$):

  • Orbit Radius: $r_n = 52.9 \left(\frac{n^2}{Z}\right)\,\text{pm}$

  • Orbit Energy: $E_n = -2.18 \times 10^{-18} \left(\frac{Z^2}{n^2}\right)\,\text{J}$

  • Negative energy value represents a bound electron state; as $n \rightarrow \infty$, $E \rightarrow 0\,\text{J}$, releasing the electron from the nucleus.