FYUGP B.Sc Chemistry Semester 1: Unit 1 - Atomic Structure

This unit covers the fundamental concepts of atomic structure, including historical developments, quantum mechanics, and the behavior of electrons in atoms. These notes are designed to help students grasp complex topics with ease.

1. Historical Development of the Structure of the Atom

The study of atomic structure has evolved over centuries. Key milestones include:

• Dalton's Atomic Theory (1808): Proposed that atoms are indivisible and indestructible.
• Thomson's Plum Pudding Model (1897): Suggested that atoms are composed of electrons embedded in a positively charged sphere.
• Rutherford's Nuclear Model (1911): Discovered the nucleus and proposed that electrons orbit around it.
• Bohr's Model (1913): Introduced quantized energy levels for electrons.

2. Bohr’s Model of the Atom

Niels Bohr proposed a model to explain the stability of atoms and the line spectrum of hydrogen. Key points:

• Electrons orbit the nucleus in specific energy levels without radiating energy.
• Electrons can jump between energy levels by absorbing or emitting energy.
• The energy of an electron in the nth orbit is given by:
  E_n = -13.6 eV / n²

Fig 1: Bohr's Model of the Atom

3. Hydrogen Atom Spectrum

The hydrogen atom emits light at specific wavelengths when electrons transition between energy levels. This results in the line emission spectrum of hydrogen.

• Lyman Series: Transitions to n=1 (ultraviolet region).
• Balmer Series: Transitions to n=2 (visible region).
• Paschen Series: Transitions to n=3 (infrared region).

4. Black Body Radiation and Photoelectric Effect

Black Body Radiation: A black body absorbs all incident radiation and emits radiation at all wavelengths. Planck's quantum theory explained this by proposing that energy is quantized.

Photoelectric Effect: When light shines on a metal surface, electrons are ejected. Einstein explained this using the concept of photons.

5. Dual Behavior of Matter and Uncertainty Principle

Matter exhibits both particle-like and wave-like properties. De Broglie proposed that particles have an associated wavelength:

λ = h / p

Heisenberg's Uncertainty Principle states that it is impossible to simultaneously determine the exact position and momentum of a particle:

Δx · Δp ≥ h/4π

6. Quantum Mechanical Approach to Atomic Structure

Quantum mechanics provides a mathematical framework to describe the behavior of electrons in atoms.

Wave Function (𝚿)

The wave function describes the quantum state of a particle. It contains all the information about the system.

• Well-Behaved Wave Function: Must be continuous, single-valued, and square-integrable.
• Normalization: The total probability of finding the particle in space must be 1.
• Orthogonality: Wave functions of different states are orthogonal.

Schrodinger Wave Equation

The Schrodinger equation describes how the wave function evolves over time:

Ĥ𝚿 = E𝚿

Where Ĥ is the Hamiltonian operator, 𝚿 is the wave function, and E is the energy.

Particle in a 1-D Box

A simple quantum mechanical model where a particle is confined to a one-dimensional box with infinite potential walls. The energy levels are quantized:

E_n = n²h² / 8mL²

Hydrogen Atom Wave Functions

The wave function for the hydrogen atom is divided into radial and angular parts:

• Radial Wave Function: Describes the probability distribution as a function of distance from the nucleus.
• Angular Wave Function: Describes the orientation of the orbital.

7. Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and electrons:

• Principal Quantum Number (n): Determines the energy level.
• Azimuthal Quantum Number (l): Determines the shape of the orbital.
• Magnetic Quantum Number (m): Determines the orientation of the orbital.
• Spin Quantum Number (s): Describes the spin of the electron.

8. Pauli’s Exclusion Principle

No two electrons in an atom can have the same set of quantum numbers.

9. Hund’s Rule of Maximum Multiplicity

Electrons fill degenerate orbitals singly before pairing up.

10. Aufbau’s Principle and Its Limitations

Electrons fill orbitals in order of increasing energy. However, exceptions occur due to electron-electron interactions.

These notes provide a comprehensive overview of atomic structure. For further reading, refer to your textbook and practice problems to solidify your understanding.