Bohr Model of Atom - Postulates

1. An electron revolves around the nucleus in certain fixed energy levels or orbits.

2. Each orbit has a specific energy associated with it, known as the energy level or quantized energy.

3. An electron can absorb or emit energy only in discrete quantities or packets called quanta.

4. The energy of an electron in an orbit is given by En = -13.6/n^2 eV, where n is the principal quantum number.

5. An electron can jump from one energy level to another by absorbing or emitting energy equal to the difference in energy between the two levels.

Bohr Model of Atom - Limitations

• Failed to explain the origin of the quantized energy levels.
• Did not accurately predict the energy levels for atoms with more than one electron.
• Could not explain the splitting of spectral lines under external magnetic fields.
• Failed to incorporate the wave-particle duality of electrons.

Quantum Mechanical Model of Atom - Introduction

• Proposed by Schrödinger in 1926
• Considers the behavior of electrons as both particles and waves
• Uses wave equations to describe the probability distribution of an electron in an atom
• Provides a more accurate description of the electron’s position and energy in an atom

Quantum Mechanical Model of Atom - Key Concepts

• Wave function: Describes the probability distribution of an electron in an atom.
• Orbitals: Regions in space where electrons are most likely to be found.
• Quantum numbers: Specify the energy, shape, and orientation of an orbital, and the spin of an electron.
• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.
• Aufbau Principle: Electrons fill the lowest energy orbitals first before going to higher energy levels.

Quantum Numbers

1. Principal Quantum Number (n): Determines the energy level or shell of an electron.

2. Angular Momentum Quantum Number (l): Determines the shape of an orbital within a shell.

3. Magnetic Quantum Number (ml): Determines the orientation of an orbital.

4. Spin Quantum Number (ms): Determines the spin state of an electron.

Orbital Shapes

• s orbitals: Spherical in shape, maximum of 2 electrons.
• p orbitals: Dumbbell-shaped, 3 mutually perpendicular p orbitals in each energy level, maximum of 6 electrons.
• d orbitals: Complex and intricate shapes, 5 d orbitals in each energy level, maximum of 10 electrons.
• f orbitals: Complex and intricate shapes, 7 f orbitals in each energy level, maximum of 14 electrons.

Electron Configuration

• Represents the arrangement of electrons in an atom.
• Follows the Aufbau principle and the Pauli exclusion principle.
• Written in the form: [noble gas] + valence electrons configuration.
• Example: Carbon (atomic number 6) electron configuration: 1s² 2s² 2p².

Atomic Spectra

• When atoms are excited, electrons can jump from lower energy levels to higher energy levels.
• When these electrons return to their original energy level, they emit energy in the form of electromagnetic radiation.
• This emitted radiation appears as discrete lines in the electromagnetic spectrum, forming the atomic spectra.
• Each element has a unique atomic spectrum that can be used for identification.

Bohr Model of Atom - Hypothesis Of Bohr

• Proposed by Niels Bohr in 1913
• Based on Rutherford’s model of atom
• Succeeded in explaining the stability of atoms
• Considered electrons to revolve around the nucleus in certain fixed orbits
• Electrons do not radiate energy while in these orbits

Bohr Model of Atom - Postulates

• An electron revolves around the nucleus in certain fixed energy levels or orbits.
• Each orbit has a specific energy associated with it, known as the energy level or quantized energy.
• An electron can absorb or emit energy only in discrete quantities or packets called quanta.
• The energy of an electron in an orbit is given by En = -13.6/n^2 eV, where n is the principal quantum number.
• An electron can jump from one energy level to another by absorbing or emitting energy equal to the difference in energy between the two levels.

Bohr Model of Atom - Limitations

• Failed to explain the origin of the quantized energy levels.
• Did not accurately predict the energy levels for atoms with more than one electron.
• Could not explain the splitting of spectral lines under external magnetic fields.
• Failed to incorporate the wave-particle duality of electrons.
• Did not consider the effects of electron-electron interactions.

Quantum Mechanical Model of Atom - Introduction

• Proposed by Schrödinger in 1926
• Considers the behavior of electrons as both particles and waves
• Uses wave equations to describe the probability distribution of an electron in an atom
• Provides a more accurate description of the electron’s position and energy in an atom
• Successfully explains the stability and properties of atoms

Quantum Mechanical Model of Atom - Key Concepts

• Wave function: Describes the probability distribution of an electron in an atom.
• Orbitals: Regions in space where electrons are most likely to be found.
• Quantum numbers: Specify the energy, shape, and orientation of an orbital, and the spin of an electron.
• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.
• Aufbau Principle: Electrons fill the lowest energy orbitals first before going to higher energy levels.

Quantum Numbers

• Principal Quantum Number (n): Determines the energy level or shell of an electron.
• Angular Momentum Quantum Number (l): Determines the shape of an orbital within a shell.
• Magnetic Quantum Number (ml): Determines the orientation of an orbital.
• Spin Quantum Number (ms): Determines the spin state of an electron.
• Quantum numbers are integral or half-integral values that provide information about the electron’s characteristics.

Orbital Shapes

• s orbitals: Spherical in shape, maximum of 2 electrons.
• p orbitals: Dumbbell-shaped, 3 mutually perpendicular p orbitals in each energy level, maximum of 6 electrons.
• d orbitals: Complex and intricate shapes, 5 d orbitals in each energy level, maximum of 10 electrons.
• f orbitals: Complex and intricate shapes, 7 f orbitals in each energy level, maximum of 14 electrons.
• Each orbital can hold a specific number of electrons based on its shape and energy level.

Electron Configuration

• Represents the arrangement of electrons in an atom.
• Follows the Aufbau principle and the Pauli exclusion principle.
• Written in the form: [noble gas] + valence electrons configuration.
• Example: Carbon (atomic number 6) electron configuration: 1s^2 2s^2 2p^2.
• Electron configurations help predict the chemical behavior and properties of elements.

Atomic Spectra

• When atoms are excited, electrons can jump from lower energy levels to higher energy levels.
• When these electrons return to their original energy level, they emit energy in the form of electromagnetic radiation.
• This emitted radiation appears as discrete lines in the electromagnetic spectrum, forming the atomic spectra.
• Each element has a unique atomic spectrum that can be used for identification.
• The atomic spectrum provides information about the energy levels and transitions of electrons in an atom.

Applications of Quantum Mechanics

• Quantum mechanics has revolutionized our understanding of the microscopic world and has wide-ranging applications.
• It is essential for understanding the behavior of atoms, molecules, and subatomic particles.
• It forms the basis for many modern technologies, including lasers, semiconductors, and nuclear technology.
• Quantum mechanics is used in fields like chemistry, materials science, quantum computing, and telecommunications.
• It continues to be an active area of research, leading to new insights and discoveries.

Bohr Model of Atom - Evidence

• The Bohr model successfully explained the spectra of hydrogen atom.
• It accurately predicted the wavelengths of spectral lines in hydrogen.
• The model provided a quantitative explanation for the Balmer series and other series of spectral lines.
• It was also supported by experimental observations of atomic emission and absorption spectra.

Quantum Mechanical Model of Atom - Wave Particle Duality

• Electrons exhibit both wave-like and particle-like behaviors.
• This phenomenon is known as wave-particle duality.
• The wave nature of electrons is described by their probability waves or wave functions.
• The particle nature of electrons is evident in their discrete energy levels and orbits.
• The quantum mechanical model successfully incorporates both aspects of electron behavior.

Quantum Mechanical Model of Atom - Uncertainty Principle

• The uncertainty principle, proposed by Heisenberg, states that there are inherent limits to our ability to measure certain pairs of physical properties simultaneously.
• It implies that we cannot precisely determine both the position and momentum of an electron at the same time.
• This principle arises due to the wave-like nature of electrons and the uncertainty in their position and momentum.
• The uncertainty principle has profound implications for our understanding of quantum mechanics.

Quantum Mechanical Model of Atom - Schrödinger Equation

• The Schrödinger equation is the fundamental equation of quantum mechanics.
• It describes the behavior of electron wave functions and their evolution over time.
• The equation is a differential equation that incorporates the Hamiltonian operator, representing the total energy of the system.
• Solving the Schrödinger equation yields the wave functions and energy levels of electrons in an atom.
• The wave functions give the probability distribution of finding an electron in different regions of space.

Quantum Mechanical Model of Atom - Orbitals

• Orbitals are regions in space where electrons are most likely to be found.
• They are described by three quantum numbers: principal quantum number (n), angular momentum quantum number (l), and magnetic quantum number (ml).
• The principal quantum number determines the energy level or shell of the orbital.
• The angular momentum quantum number determines the shape of the orbital.
• The magnetic quantum number determines the orientation of the orbital in space.

Quantum Mechanical Model of Atom - Electron Spin

• Electron spin is an intrinsic property of electrons.
• It is described by the spin quantum number (ms).
• The spin quantum number can have two values: +1/2 (spin-up) and -1/2 (spin-down).
• Spin influences the magnetic properties and behavior of electrons in atoms.
• The Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers, including spin.

Quantum Mechanical Model of Atom - Energy Levels and Transitions

• The energy levels in the quantum mechanical model are quantized and discrete.
• Electrons occupy these energy levels in accordance with the Aufbau principle.
• Energy transitions occur when electrons move between energy levels.
• Absorption of energy by an electron causes it to jump to a higher energy level.
• Emission of energy by an electron causes it to drop to a lower energy level, emitting the excess energy as electromagnetic radiation.

Quantum Mechanical Model of Atom - Electron Configurations

• Electron configurations describe the arrangement of electrons in an atom.
• They follow the Aufbau principle, filling orbitals in order of increasing energy.
• Hund’s rule states that orbitals of the same energy are filled with single electrons before pairing occurs.
• Electron configurations can be represented using the noble gas notation, indicating the previous noble gas followed by the valence electrons.
• Example: Oxygen (atomic number 8) electron configuration: [He] 2s^2 2p^4.

Quantum Mechanical Model of Atom - Periodic Table

• The periodic table is organized based on electron configurations.
• Elements with similar electron configurations exhibit similar chemical properties.
• The periods correspond to the energy levels or shells of electrons.
• The groups or columns correspond to the valence electrons and have similar chemical behavior.
• Understanding electron configurations helps predict the periodic trends and behavior of elements in the periodic table.

Comparison: Bohr Model vs. Quantum Mechanical Model

• Bohr Model:

  • Electrons revolve in fixed orbits with specific energies.
  • Failed to explain some observations and limitations.
  • Provided initial understanding of atomic structure.

• Quantum Mechanical Model:

  • Describes electrons as waves and particles.
  • Incorporates wave-particle duality and uncertainty principle.
  • Provides accurate descriptions of electron behavior and energy levels.
  • Helps understand the periodic table and chemical properties of elements.