Bohr Model of Atom

• Proposed by Danish physicist Niels Bohr in 1913.
• Explains the structure of atoms and electron energy levels.
• Essential for understanding atomic physics.
• Provides a framework for explaining atomic spectra.

Bohr Model for Hydrogen Atom

• Bohr applied his model to the hydrogen atom.
• According to Bohr, electrons revolve around the nucleus in discrete circular orbits.
• Only certain orbits are allowed and correspond to specific energy levels.
• Electrons can transition between energy levels by absorbing or emitting energy.

Calculation of Radius and Velocity for Hydrogen Atom

• The radius of an electron’s orbit can be calculated using Bohr’s formula: r = (0.529 Å) * n² / Z
  • r: radius of the orbit
  • n: principal quantum number
  • Z: atomic number of the nucleus
  • 0.529 Å: Bohr radius
• The velocity of an electron in the orbit can be calculated using the formula: v = 2.18 x 10⁶ m/s / n
  • v: velocity of the electron
  • 2.18 x 10⁶ m/s: constant value
  • n: principal quantum number

Example:

• Calculate the radius and velocity of the electron in the n = 1 energy level of a hydrogen atom.
• Given:
  • Z (atomic number) = 1
  • n = 1
• Solution:
  • Using the radius formula: r = (0.529 Å) * n² / Z
    • r = (0.529 Å) * 1² / 1 = 0.529 Å
  • Using the velocity formula: v = 2.18 x 10⁶ m/s / n
    • v = 2.18 x 10⁶ m/s / 1 = 2.18 x 10⁶ m/s

Bohr Model of Atom - Atomic Spectra

• Bohr’s model successfully explains the emission and absorption spectra of atoms.
• When an electron moves from a higher-energy level to a lower-energy level, it emits energy in the form of light (emission spectrum).
• The emitted light consists of spectral lines corresponding to the energy difference between the two levels.
• When an electron absorbs energy, it moves from a lower-energy level to a higher-energy level, resulting in an absorption spectrum.

Bohr Model of Atom - Limitations

• Bohr’s model has some limitations:
  • Does not explain the behavior of atoms with more than one electron.
  • Neglects the wave nature of electrons, treating them as particles.
  • Fails to explain the fine structure of spectral lines.
  • Does not account for the existence of subshells and orbitals.

Summary

• Bohr’s model of the atom provides a simplified understanding of electron behavior.
• It explains the quantized energy levels and the emission/absorption spectra of atoms.
• The radius and velocity of electron orbits in the hydrogen atom can be calculated using Bohr’s formulas.
• However, the model has limitations and does not fully explain the complex structure of atoms.

Bohr Model of Atom - Atomic Spectra

• Bohr’s model successfully explains the emission and absorption spectra of atoms.
• When an electron moves from a higher-energy level to a lower-energy level, it emits energy in the form of light (emission spectrum).
• The emitted light consists of spectral lines corresponding to the energy difference between the two levels.
• When an electron absorbs energy, it moves from a lower-energy level to a higher-energy level, resulting in an absorption spectrum.

Bohr Model of Atom - Limitations

• Bohr’s model has some limitations:
  • Does not explain the behavior of atoms with more than one electron.
  • Neglects the wave nature of electrons, treating them as particles.
  • Fails to explain the fine structure of spectral lines.
  • Does not account for the existence of subshells and orbitals.
• Despite these limitations, Bohr’s model was a significant step toward understanding atomic structure.

Quantum Mechanics

• Quantum mechanics is a branch of physics that deals with the behavior of particles at the atomic and subatomic level.
• It provides a more accurate description of electron behavior compared to the Bohr model.
• Quantum mechanics introduced the concept of wave-particle duality, where particles exhibit both wave-like and particle-like properties.
• The behavior of electrons is described by wavefunctions and probability distributions.

Quantum Numbers

• Quantum numbers are used to describe the properties of electrons in an atom.
• There are four quantum numbers:
  1. Principal quantum number (n): indicates the energy level or shell the electron occupies.
  2. Angular momentum quantum number (l): determines the shape of the orbital.
  3. Magnetic quantum number (ml): specifies the orientation of the orbital in space.
  4. Spin quantum number (ms): describes the spin of the electron (+1/2 or -1/2).

Pauli Exclusion Principle

• The Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers.
• This means that in a given energy level or orbital, there can be a maximum of two electrons with opposite spins.
• The principle helps explain the stability and organization of electron configurations in atoms.

Electron Configurations

• Electron configurations describe how electrons are arranged in an atom.
• The Aufbau principle states that electrons fill the lowest energy levels first before occupying higher energy levels.
• The filling order follows the diagonal rule, where electrons fill orbitals in a specific pattern based on their quantum numbers.
• Electron configurations are written using the specific notation: 1s² 2s² 2p⁶, where each superscript represents the number of electrons in a specific subshell.

Example:

• Write the electron configuration for nitrogen.
• Solution:
  • Nitrogen has an atomic number of 7, meaning it has 7 electrons.
  • The electron configuration can be written as: 1s² 2s² 2p³.
  • This indicates that there are 2 electrons in the 1s orbital, 2 electrons in the 2s orbital, and 3 electrons in the 2p orbital.

Valence Electrons

• Valence electrons are the electrons in the outermost energy level of an atom.
• They are involved in chemical bonding and determining the chemical properties of an element.
• The number of valence electrons can be determined from the electron configuration.
• For example, carbon (atomic number 6) has an electron configuration of 1s² 2s² 2p², so it has 4 valence electrons.

Lewis Dot Structures

• Lewis dot structures are a way to represent the valence electrons of an atom.
• In a Lewis dot structure, the symbol of the element is surrounded by dots representing the valence electrons.
• The dots are arranged around the symbol, with a maximum of 8 dots (octet rule) to satisfy the stability of the atom.
• Lewis dot structures are useful for understanding and predicting chemical bonding.

Bohr Model of Atom - Bohr Model for Hydrogen atom, Radius & Velocity Calculation

Bohr Model for Hydrogen Atom

• Electrons revolve around the nucleus in discrete circular orbits.
• Only certain orbits are allowed and correspond to specific energy levels.
• Electrons can transition between energy levels by absorbing or emitting energy.
• This behavior is consistent with the observation of atomic spectra.

Calculation of Radius and Velocity for Hydrogen Atom

• The radius of an electron’s orbit can be calculated using Bohr’s formula: r = (0.529 Å) * n² / Z
  • r: radius of the orbit
  • n: principal quantum number
  • Z: atomic number of the nucleus
  • 0.529 Å: Bohr radius
• The velocity of an electron in the orbit can be calculated using the formula: v = 2.18 x 10⁶ m/s / n
  • v: velocity of the electron
  • 2.18 x 10⁶ m/s: constant value
  • n: principal quantum number

Example 1:

• Calculate the radius and velocity of the electron in the n = 2 energy level of a hydrogen atom.
• Given:
  • Z (atomic number) = 1
  • n = 2
• Solution:
  • Using the radius formula: r = (0.529 Å) * n² / Z
    • r = (0.529 Å) * 2² / 1 = 2.116 Å
  • Using the velocity formula: v = 2.18 x 10⁶ m/s / n
    • v = 2.18 x 10⁶ m/s / 2 = 1.09 x 10⁶ m/s

Example 2:

• Calculate the radius and velocity of the electron in the n = 3 energy level of a hydrogen atom.
• Given:
  • Z (atomic number) = 1
  • n = 3
• Solution:
  • Using the radius formula: r = (0.529 Å) * n² / Z
    • r = (0.529 Å) * 3² / 1 = 4.243 Å
  • Using the velocity formula: v = 2.18 x 10⁶ m/s / n
    • v = 2.18 x 10⁶ m/s / 3 = 0.726 x 10⁶ m/s

Bohr Model of Atom - Atomic Spectra

• When an electron moves from a higher-energy level to a lower-energy level, it emits energy in the form of light (emission spectrum).
• The emitted light consists of spectral lines corresponding to the energy difference between the two levels.
• When an electron absorbs energy, it moves from a lower-energy level to a higher-energy level, resulting in an absorption spectrum.
• The emission and absorption spectra provide important information about the energy levels of atoms.

Bohr Model of Atom - Limitations

• Bohr’s model has some limitations:
  • It does not explain the behavior of atoms with more than one electron.
  • It neglects the wave nature of electrons, treating them as particles.
  • It fails to explain the fine structure of spectral lines.
  • It does not account for the existence of subshells and orbitals.
• Despite these limitations, Bohr’s model was a significant step toward understanding atomic structure.

Quantum Mechanics

• Quantum mechanics is a branch of physics that deals with the behavior of particles at the atomic and subatomic level.
• It provides a more accurate description of electron behavior compared to the Bohr model.
• Quantum mechanics introduced the concept of wave-particle duality, where particles exhibit both wave-like and particle-like properties.
• The behavior of electrons is described by wavefunctions and probability distributions.

Quantum Numbers

• Quantum numbers are used to describe the properties of electrons in an atom.
• There are four quantum numbers:
  1. Principal quantum number (n): indicates the energy level or shell the electron occupies.
  2. Angular momentum quantum number (l): determines the shape of the orbital.
  3. Magnetic quantum number (ml): specifies the orientation of the orbital in space.
  4. Spin quantum number (ms): describes the spin of the electron (+1/2 or -1/2).

Pauli Exclusion Principle

• The Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers.
• This means that in a given energy level or orbital, there can be a maximum of two electrons with opposite spins.
• The principle helps explain the stability and organization of electron configurations in atoms.