Atomic Structure, Waves, and Quantum Theory: Foundations of General Chemistry

Introduction to Atomic and Molecular Structure

Course Overview

This section introduces the foundational concepts of atomic and molecular structure, which are essential for understanding chemical phenomena at the microscopic level. Topics include the nature of matter, wave-particle duality, quantum mechanics, and the historical development of atomic theory.

• Atomic and Molecular Structure: Explains macroscopic observations using microscopic models.

• Organic Chemistry: Applies atomic theory to predict chemical reactivity.

• Kinetics and Mechanisms: Explores rates and mechanisms of chemical processes.

Particles vs. Waves

Nature of Light and Matter

Early scientific inquiry focused on whether light and matter behave as particles or waves. This distinction is fundamental to quantum mechanics and chemistry.

• Particles: Discrete packets of matter with mass and volume; may possess electric charge; interact via collisions.

• Waves: Oscillating disturbances in a medium or field; possess wavelength, frequency, and amplitude; interact via interference.

Types and Properties of Waves

Wave Characteristics

Waves are characterized by their wavelength and frequency, which determine their energy and behavior.

• Wavelength (λ): Distance between successive maxima or minima.

• Frequency (ν): Number of cycles per unit time (usually seconds).

• Relationship: $\lambda \propto \frac{1}{\nu}$ or $\lambda \nu = c$

• Speed of light: $c = 2.99 \times 10^8$ m/s

Electromagnetic Spectrum

Classification of Radiation

Electromagnetic radiation is classified by wavelength or frequency, ranging from gamma rays to radio waves. The boundaries between classes are arbitrary and based on convenience.

• Gamma rays, X-rays, Ultraviolet, Visible, Infrared, Microwaves, Radio waves

• Applications: Atomic and molecular spectroscopy, medical imaging, communications

Wave Interference

Constructive and Destructive Interference

Waves can interfere constructively (additively) or destructively (differentially), depending on phase alignment.

• Constructive interference: Waves in phase increase intensity (bright area).

• Destructive interference: Waves out of phase decrease intensity (dark spot).

The Double-Slit Experiment

Evidence for Wave Nature of Light

Thomas Young's experiment (1803) demonstrated that light passing through two slits produces an interference pattern, supporting the wave theory of light.

• Interference pattern: Alternating bright and dark bands on a screen.

• Significance: Provided strong evidence for the wave nature of light.

Historical Discoveries in Atomic Structure

Key Experiments and Models

Several landmark experiments contributed to our understanding of atomic structure.

• Faraday (1813): Charge/mass ratio of H+ = 96,487 C/g.

• Crookes (1870s): Characterized cathode rays as small, light, negatively charged particles.

• Thompson (1897): Charge/mass ratio of electron = $1.76 \times 10^8$ C/g.

• Millikan (1909): Absolute charge of electron = $1.6 \times 10^{-19}$ C; mass = $9.1 \times 10^{-31}$ g.

• Chadwick (1932): Identified the neutron.

Early Models of the Atom

Plum Pudding Model

Electrons were thought to be embedded in a positively charged 'pudding,' with the magnitude of positive charge equal to the number of electrons.

• Limitations: Could not explain experimental results from scattering experiments.

Discovery of the Nucleus

Rutherford's Gold Foil Experiment

Rutherford (1911) showed that atoms have a small, dense, positively charged nucleus by observing the scattering of alpha particles through gold foil.

• Key observation: Most alpha particles passed through, but a small fraction were deflected backward.

• Conclusion: Atoms are mostly empty space with a dense nucleus.

Probability of backscatter:

• $\text{Probability of backscatter} = \frac{\text{backscatter count rate}}{\text{incident count rate}} \times \frac{\text{area of nuclei}}{\text{area of foil}}$

Classical Description of Atoms

Problems with Planetary Model

Rutherford's model could not explain why electrons do not spiral into the nucleus due to electromagnetic radiation predicted by Maxwell's equations.

• Accelerating charged particles: Should emit EM radiation and lose energy.

• Predicted collapse time: $\sim 10^{-10}$ s

Blackbody Paradox and Quantum Theory

Planck's Solution

Classical theory predicted infinite intensity at low frequencies (ultraviolet catastrophe). Planck proposed that energy is quantized:

• $\Delta E = nh\nu$

• n: Integer

• h: Planck's constant

• ν: Frequency

Photoelectric Effect

Einstein's Explanation

Electrons are ejected from metal surfaces when exposed to light of sufficient frequency. The effect could not be explained by classical wave theory.

• Threshold frequency (ν0): Minimum frequency required to eject electrons.

• Kinetic energy of ejected electrons: $KE = \frac{1}{2}mv^2$

• Energy of photon: $E_{\text{photon}} = h\nu = \frac{hc}{\lambda}$

• Work function (φ): $KE = h\nu - h\nu_0$

Atomic Spectra and Energy Levels

Hydrogen Emission Spectrum

Electric discharge through hydrogen gas produces light at specific wavelengths, corresponding to electron transitions between energy levels.

• UV series: $n_f = 1$

• Visible series: $n_f = 2$

• IR series: $n_f = 3$

The Rydberg Equation

Predicting Spectral Lines

The Rydberg equation predicts the wavelength of spectral lines for hydrogen-like atoms:

• $\frac{1}{\lambda} = R \left( \frac{n_f^2 - n_i^2}{n_i^2 n_f^2} \right)$

• Rydberg constant: $R = 1.096776 \times 10^7$ m-1

The Bohr Model

Quantized Orbits and Energy Levels

Bohr proposed that electrons orbit the nucleus at specific, quantized distances, with angular momentum quantized:

• $m v r = \frac{n h}{2 \pi}$

• Bohr radius: $r = \frac{\epsilon_0 n^2 h^2}{\pi m_e Z e^2}$

• Energy of electron: $E_n = -2.178 \times 10^{-18} \left( \frac{Z^2}{n^2} \right)$ J/atom

• Energy change for transitions: $\Delta E = E_f - E_i = -2.178 \times 10^{-18} Z \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$

Ionization Energy

Calculating Ionization Energy

Ionization energy is the energy required to remove an electron from an atom:

• $E_{\text{ionization}} = +2.178 \times 10^{-18} \left( \frac{Z^2}{n^2} \right)$

• Note: Only valid for hydrogen-like atoms (one electron).

Practice Problem: Ionization Energy and Light

Example Calculation

Given the ionization energy of Arg is 1527 kJ/mol, calculate the lowest frequency and corresponding wavelength of light that can ionize an Ar atom:

• $E = h\nu = 1.527 \times 10^6$ J/mol

• $\nu = \frac{E}{h} = 3.828 \times 10^{15}$ s-1

• $\lambda = \frac{c}{\nu} = 7.83 \times 10^{-8}$ m = 78.3 nm (UV Region)