Bohr Model of Atom - Energy Of nth orbit & Energy level

  • Introduction to Bohr Model
  • Energy levels in an atom
  • Energy of nth orbit in hydrogen atom
  • Energy of nth orbit in multi-electron atoms
  • Factors affecting energy levels
    • Nuclear charge
    • Shielding effect
    • Orbital shape
    • Penetration effect
  • Energy level diagrams
  • Calculation of energy using Rydberg formula
  • Application of energy levels in atomic spectroscopy
  • Examples of energy calculations in different elements
  1. Energy Levels in an Atom
  • Electrons in an atom are found in specific energy levels or shells.
  • The energy levels are represented by the principal quantum number, n.
  • The lowest energy level is the ground state, represented by n = 1.
  • Each energy level can hold a maximum number of electrons based on the formula 2n^2, where n is the principal quantum number.
  • Example: The first energy level (n = 1) can hold a maximum of 2 electrons (2 x 1^2 = 2).
  1. Energy of the nth Orbit in Hydrogen Atom
  • According to Bohr’s postulates, the energy of an electron in the nth orbit of a hydrogen atom is given by the formula E = (-13.6/n^2) eV.
  • E represents the energy of the electron in the given orbit.
  • n is the principal quantum number indicating the energy level.
  • The negative sign indicates that the energy is lower as the electron gets closer to the nucleus.
  • Example: For the first energy level (n = 1), the energy of an electron is -13.6 eV.
  1. Energy of the nth Orbit in Multi-electron Atoms
  • In multi-electron atoms, the energy of the nth orbit is influenced not only by the principal quantum number, but also by other factors such as effective nuclear charge and shielding effect.
  • The energy levels get closer together as the number of electrons increases, leading to the splitting of energy levels.
  • Calculation of energy levels in multi-electron atoms becomes more complex due to the interactions between electrons.
  1. Factors Affecting Energy Levels
  • Nuclear charge: The stronger the nuclear charge, the more energy is required to remove an electron from an atom.
  • Shielding effect: Inner electrons shield the outer electrons from the full attraction of the nucleus, affecting the energy levels.
  • Orbital shape: Different orbitals have different energies due to their shape and proximity to the nucleus.
  • Penetration effect: Electrons in certain orbitals can penetrate closer to the nucleus, resulting in lower energy levels.
  1. Energy Level Diagrams
  • Energy level diagrams are graphical representations of the electron energy levels in an atom.
  • Each energy level is represented by a horizontal line.
  • The lines are labeled with the principal quantum numbers.
  • Electrons are represented as arrows pointing up or down, indicating their electron spin.
  • Example: Oxygen atom energy level diagram would show 1s^2 2s^2 2p^4 configuration.
  1. Calculation of Energy using Rydberg Formula
  • The Rydberg formula is used to calculate the energy difference between two energy levels in an atom.
  • It is given by the equation: ∆E = Rh (1/nf^2 - 1/ni^2), where ∆E represents the energy change, Rh is the Rydberg constant, nf is the final quantum number, and ni is the initial quantum number.
  • The Rydberg constant is approximately 2.18 × 10^-18 J.
  1. Application of Energy Levels in Atomic Spectroscopy
  • Atomic spectroscopy involves studying the interaction between electromagnetic radiation and atoms.
  • Energy levels play a crucial role in the absorption and emission of light by atoms.
  • Each element has a unique set of energy levels, leading to characteristic spectral lines.
  • Atomic spectroscopy is useful for identifying elements and analyzing their concentration in a sample.
  1. Example: Calculation of Energy Levels in Hydrogen Atom
  • Given: Hydrogen atom, principal quantum number (n) = 2
  • Using the energy formula E = (-13.6/n^2) eV,
  • Energy in the second energy level (n = 2) = -13.6/2^2 = -3.4 eV
  • Thus, the energy of an electron in the second energy level of a hydrogen atom is -3.4 eV.
  1. Example: Calculation of Energy Change using Rydberg Formula
  • Given: Rh = 2.18 × 10^-18 J, nf = 3, ni = 2
  • Using the Rydberg formula ∆E = Rh (1/nf^2 - 1/ni^2),
  • Energy change (∆E) = 2.18 × 10^-18 J (1/3^2 - 1/2^2)
  • ∆E ≈ 2.18 × 10^-18 J (1/9 - 1/4) = 1.75 × 10^-19 J
  • Therefore, the energy change between the second and third energy levels is approximately 1.75 × 10^-19 J.
  1. Examples of Energy Calculations in Different Elements
  • Energy calculations can be performed for different elements using their respective atomic configurations and energy level diagrams.
  • These calculations help determine the stability of atoms and their reactivity.
  • Examples include energy calculations for hydrogen, helium, carbon, and oxygen atoms.
  • These calculations provide insights into the behavior of elements in chemical reactions and bonding.
  1. Applications of Energy Calculations in Chemistry
  • Energy calculations in atoms and molecules help understand chemical reactions and bonding.
  • Calculation of bond energy in covalent compounds.
  • Calculation of ionization energy and electron affinity in elements.
  • Determination of molecular orbital energy levels.
  • Calculation of energy changes in chemical reactions.
  1. Calculation of Bond Energy in Covalent Compounds
  • Bond energy is the energy required to break a bond between two atoms in a covalent compound.
  • It is calculated by subtracting the energy of the individual atoms from the energy of the bonded atoms.
  • Example: The bond energy of a carbon-carbon double bond is determined by calculating the energy difference between two isolated carbon atoms and the bonded carbon atoms.
  1. Calculation of Ionization Energy in Elements
  • Ionization energy is the energy required to remove an electron from a neutral atom.
  • It can be calculated using the formula E = (-13.6/n^2) eV for hydrogen atom.
  • Example: The ionization energy of a hydrogen atom in its ground state (n = 1) is -13.6 eV.
  1. Calculation of Electron Affinity in Elements
  • Electron affinity is the energy released when an electron is added to a neutral atom.
  • It can be calculated using the formula E = (-13.6/n^2) eV for hydrogen atom.
  • Example: The electron affinity of a hydrogen atom in its first excited state (n = 2) is -3.4 eV.
  1. Determination of Molecular Orbital Energy Levels
  • Molecular orbital theory describes the distribution of electrons in molecules.
  • Energy calculations help determine the energy levels of molecular orbitals.
  • Higher energy levels represent the anti-bonding molecular orbitals, while lower energy levels represent the bonding molecular orbitals.
  • Examples: Determining the energy levels in a diatomic molecule like O2 or N2.
  1. Calculation of Energy Changes in Chemical Reactions
  • Energy calculations are crucial in determining the energy changes during chemical reactions.
  • Energy changes include enthalpy change (∆H), entropy change (∆S), and free energy change (∆G).
  • Example: Calculating the energy change during the combustion of methane (CH4) to form carbon dioxide (CO2) and water vapor (H2O).
  1. Example: Calculation of Bond Energy in HCl
  • Given: H-Cl bond dissociation energy = 431 kJ/mol
  • Bond energy is the average energy required to break a bond.
  • The bond energy of the H-Cl bond in HCl is 431 kJ/mol.
  1. Example: Calculation of Ionization Energy in Lithium Atom
  • Given: Lithium atom, principal quantum number (n) = 2
  • Using the ionization energy formula E = (-13.6/n^2) eV,
  • Ionization energy of a lithium atom = -13.6/2^2 = -3.4 eV
  • Therefore, the ionization energy of a lithium atom in its ground state is approximately -3.4 eV.
  1. Example: Calculation of Electron Affinity in Chlorine Atom
  • Given: Chlorine atom, principal quantum number (n) = 2
  • Using the electron affinity formula E = (-13.6/n^2) eV,
  • Electron affinity of a chlorine atom = -13.6/2^2 = -3.4 eV
  • Therefore, the electron affinity of a chlorine atom in its first excited state is approximately -3.4 eV.
  1. Example: Calculation of Energy Change in Combustion Reaction
  • Given: Combustion of methane (CH4) to form CO2 and H2O
  • The enthalpy change (∆H) can be calculated by subtracting the energy of the reactants from the energy of the products.
  • The entropy change (∆S) and free energy change (∆G) can be determined using the equations relating to entropy and free energy.
  • Example calculation and determination of the energy change in the combustion of methane.