Structure of Atom

Learning Objectives

• Understand the quantum mechanical model of the atom, including the nature of electromagnetic radiation, Planck's quantum theory, and the photoelectric effect.
• Describe and analyze the Thomson, Rutherford, and Bohr atomic models.
• Explore the wave nature of electromagnetic radiation and Planck's quantum theory, including calculations involving wave equations ($c = \nu\lambda$) and energy equations ($E = h\nu$).
• Analyze the photoelectric effect, including Einstein's explanation using quantum theory and the calculation of kinetic energy of ejected electrons.
• Study emission and absorption spectra, focusing on the line spectra of hydrogen and the Rydberg formula for spectral lines.
• Understand the dual behavior of matter and the Heisenberg Uncertainty Principle, including the de Broglie wavelength equation ($\lambda = h/mv$).
• Learn about the discovery and characterization of sub-atomic particles, including experiments like the cathode ray tube and Millikan's oil drop experiment.
• Examine Bohr's model for the hydrogen atom, including quantized orbits and the calculation of energy levels using the Rydberg constant.
• Study quantum numbers and the shapes of orbitals, including Principal ($n$), Azimuthal ($l$), Magnetic ($m_l$), and Spin ($m_s$) quantum numbers.
• Apply rules for filling orbitals and electronic configuration, including the Aufbau Principle, Pauli Exclusion Principle, and Hund's Rule of Maximum Multiplicity.
• Calculate and interpret atomic number, mass number, isotopes, and isobars, including symbolic representation of atoms/ions.

Chapter Notes

Quantum Mechanical Model of Atom

• Electromagnetic Radiation: Light and other forms of electromagnetic radiation exhibit both wave-like and particle-like properties.
• Planck's Quantum Theory: Energy is quantized and can be emitted or absorbed in discrete units called quanta.
• Photoelectric Effect: Explained by Einstein using quantum theory; electrons are ejected from metal surfaces when exposed to light of a certain frequency.

Atomic Models

• Thomson Model: Proposed a "plum pudding" model where electrons are embedded in a positively charged sphere.
• Rutherford Model: Introduced the nuclear model with a dense, positively charged nucleus surrounded by electrons.
• Bohr Model: Electrons orbit the nucleus in fixed paths with quantized energy levels.

Wave Nature of EM Radiation & Planck's Quantum Theory

• Electromagnetic Spectrum: Includes various types of radiation distinguished by wavelength and frequency.
• Wave Calculations: $c = \nu\lambda$, where $c$ is the speed of light, $\nu$ is frequency, and $\lambda$ is wavelength.
• Energy Calculations: $E = h\nu$, where $h$ is Planck's constant.

Photoelectric Effect

• Einstein's Explanation: Light consists of photons; energy of photons is proportional to their frequency.
• Kinetic Energy of Ejected Electrons: $KE = h\nu - W_0$, where $W_0$ is the work function of the metal.

Atomic Spectra

• Emission and Absorption Spectra: Atoms emit or absorb light at specific wavelengths, producing line spectra.
• Rydberg Formula: Describes the wavelengths of spectral lines in hydrogen: $\frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$.

Dual Behavior of Matter & Heisenberg Uncertainty Principle

• de Broglie Wavelength: $\lambda = \frac{h}{mv}$, where $m$ is mass and $v$ is velocity.
• Heisenberg Uncertainty Principle: It is impossible to simultaneously know the exact position and momentum of a particle.

Discovery of Sub-Atomic Particles

• Electron: Discovered by J.J. Thomson using cathode ray tube experiments.
• Proton: Discovered by Rutherford through gold foil experiment.
• Neutron: Discovered by Chadwick through beryllium bombardment experiments.

Bohr's Model for Hydrogen Atom

• Quantized Orbits: Electrons move in fixed orbits with specific energies.
• Energy Levels: Calculated using $E_n = -\frac{R_H}{n^2}$, where $R_H$ is the Rydberg constant.

Quantum Numbers and Shapes of Orbitals

• Principal Quantum Number ($n$): Indicates the size and energy level of the orbital.
• Azimuthal Quantum Number ($l$): Defines the shape of the orbital.
• Magnetic Quantum Number ($m_l$): Specifies the orientation of the orbital.
• Spin Quantum Number ($m_s$): Describes the spin of the electron.

Rules for Filling Orbitals & Electronic Configuration

• Aufbau Principle: Electrons fill orbitals starting from the lowest energy level.
• Pauli Exclusion Principle: No two electrons can have the same set of four quantum numbers.
• Hund's Rule: Electrons fill degenerate orbitals singly before pairing.

Atomic Number, Mass Number, Isotopes and Isobars

• Atomic Number ($Z$): Number of protons in the nucleus.
• Mass Number ($A$): Total number of protons and neutrons.
• Isotopes: Atoms with the same atomic number but different mass numbers.
• Isobars: Atoms with the same mass number but different atomic numbers.