- Introduction to Bohr Model
- Explanation of Energy Levels
- Derivation of Bohr Formula
- Understanding Angular Momentum
- Quantization of Angular Momentum
Introduction to Bohr Model
- Proposed by Niels Bohr in 1913
- Describes behavior of electrons in atoms
- Based on quantum theory
- Provides explanation for atomic spectra
- Lays foundation for modern atomic theory
Explanation of Energy Levels
- Electrons move in specific orbits around the nucleus
- Each orbit represents a specific energy level
- Electrons can move between energy levels by absorbing or emitting energy
- Higher energy levels are farther from the nucleus
- Bohr proposed that the angular momentum of electron is quantized
- Angular momentum is given by L = n * h / 2π
- n is the principal quantum number
- h is the Planck’s constant (6.62607015 × 10^-34 Js)
- Angular momentum is quantized in multiples of h / 2π
Understanding Angular Momentum
- Angular momentum is a vector quantity
- It depends on the mass, velocity, and distance from the axis of rotation
- For electron, mass is negligible compared to the nucleus
- Angular momentum can be expressed as mvr
- v is the linear velocity of the electron
- r is the distance between the electron and nucleus
Quantization of Angular Momentum
- Bohr proposed that angular momentum is quantized in units of h / 2π
- This implies that the product of mass, velocity, and radius must be quantized
- Angular momentum quantization explains stable orbits of electron
- Only certain values of angular momentum are allowed
- These correspond to different energy levels in the atom
Energy Levels in Hydrogen Atom
- For hydrogen atom, the energy levels are given by E = -13.6/n^2 eV
- E is the energy of the orbit
- n is the principal quantum number
- Each energy level corresponds to a specific orbit
Calculation of Radius
- Radius of the orbit can be calculated using the formula r = 0.529 Å * n^2 / Z
- r is the radius of the orbit
- Z is the atomic number
- 0.529 Å is the Bohr radius
Limitations of the Bohr Model
- Only applicable to hydrogen atom
- Does not explain behavior of multi-electron atoms
- Violates Heisenberg’s uncertainty principle
- Fails to explain spectral lines with fine structure
- Limited accuracy in predicting energy levels
Example Calculation
Consider a hydrogen atom with n = 3.
- Energy of the orbit: E = -13.6 / 3^2 eV = -1.51 eV
- Radius of the orbit: r = 0.529 Å * 3^2 / 1 = 1.59 Å
Atomic Structure
- Introduction to atomic structure
- Protons, neutrons, and electrons
- Atomic number and mass number
- Isotopes and atomic mass
- Electron configuration
Wave-particle Duality
- Dual nature of matter and energy
- Wave properties of electrons and photons
- Particle properties of electrons and photons
- Wave-particle duality experiment
- De Broglie wavelength
Quantum Mechanics
- Introduction to quantum mechanics
- Schrödinger equation
- Wavefunctions and probability densities
- Quantum numbers
- Pauli exclusion principle
Quantum Mechanical Model of Atom
- Orbitals and subshells
- Electron spin and magnetic quantum number
- Aufbau principle
- Hund’s rule
- Electronic configuration examples
Periodic Table
- Structure and organization of periodic table
- Periods and groups
- Block and series
- Trends in atomic properties
- Periodic properties and periodicity
Electron Affinity and Ionization Energy
- Definition and trends of electron affinity
- Factors affecting electron affinity
- Definition and trends of ionization energy
- Factors affecting ionization energy
- Importance of electron affinity and ionization energy
Electromagnetic Waves
- Electromagnetic spectrum
- Properties of electromagnetic waves
- Relationship between wavelength, frequency, and energy
- Speed of light
- Applications of electromagnetic waves
Atomic Spectra
- Definition and types of atomic spectra
- Line spectra and continuous spectra
- Emission and absorption spectra
- Relation between energy and spectra
- Importance of atomic spectra in studying atoms
Quantum Numbers
- Principal quantum number (n)
- Angular momentum quantum number (l)
- Magnetic quantum number (ml)
- Spin quantum number (ms)
- Explanation and examples of quantum numbers
Electron Configuration
- Rules for filling electron orbitals
- Aufbau principle and filling order
- Pauli exclusion principle and spin pairing
- Hund’s rule and maximum multiplicity
- Examples of electron configuration
Newton’s Laws of Motion
- Newton’s First Law of Motion
- An object at rest stays at rest, and an object in motion stays in motion with the same velocity, unless acted upon by a net external force.
- Newton’s Second Law of Motion
- The acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
- Newton’s Third Law of Motion
- For every action, there is an equal and opposite reaction.
Projectile Motion
- Definition of projectile motion
- Horizontal and vertical components
- Range of a projectile
- Maximum height of a projectile
- Angle of projection
Circular Motion
- Uniform circular motion
- Centripetal force and centripetal acceleration
- Relationship between radius, angular velocity, and linear velocity
- Examples of circular motion in daily life
- Banking of roads
Work, Power, and Energy
- Definition of work
- Calculation of work done by a constant force
- Kinetic energy and potential energy
- Conservation of mechanical energy
- Definition of power
Gravitation
- Universal law of gravitation
- Calculation of gravitational force
- Gravitational field strength and potential
- Kepler’s laws of planetary motion
- Escape velocity
Waves and Sound
- Characteristics of waves
- Transverse and longitudinal waves
- Wave speed, frequency, and wavelength
- Sound waves and their properties
- Doppler effect
Optics
- Reflection and refraction of light
- Law of reflection and Snell’s law
- Types of lenses and mirrors
- Image formation by lenses and mirrors
- Lens formula and mirror formula
Electric Charges and Fields
- Electric charge and its properties
- Coulomb’s law and electric field intensity
- Electric field lines and electric dipole
- Gauss’s law and electric flux
- Electric potential and potential energy
Electromagnetic Induction
- Faraday’s laws of electromagnetic induction
- Lenz’s law and induced emf
- Self-inductance and mutual inductance
- Applications of electromagnetic induction
- Transformers and generators
Modern Physics
- Photoelectric effect and wave-particle duality
- Planck’s quantum theory of radiation
- Bohr’s model of hydrogen atom
- Dual nature of matter and de Broglie’s hypothesis
- Nuclear physics and radioactivity