Bohr Model of Atom-I – An introduction
- Developed by Niels Bohr in 1913
- Explains stability and line spectrum of hydrogen atom
- Based on Planck’s quantum theory and Rutherford’s nuclear model
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Bohr Model of Atom-II – Assumptions
- Electrons revolve in circular orbits around the nucleus
- Electrons can only exist in certain discrete energy levels
- Electrons can jump to higher or lower energy levels by absorbing or emitting energy respectively
- Electrons in stable orbits do not radiate energy
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Bohr Model of Atom-III – Energy Levels
- Energy levels denoted by ’n’ (principal quantum number)
- Energy of each level increases as ’n’ increases
- Ground state (n = 1) has minimum energy
- Higher energy levels have more orbits and are farther from the nucleus
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Bohr Model of Atom-IV – Energy Transitions
- Electrons exhibit stable orbits at certain energy levels
- When an electron transitions between energy levels, energy is absorbed or emitted
- Emission: Electron jumps to lower energy level and emits energy in the form of photon
- Absorption: Electron jumps to higher energy level by absorbing energy
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Bohr Model of Atom-V – Line Spectrum
- Line spectrum: Emission or absorption of energy results in the appearance of a spectrum with discrete lines
- Each line represents a specific energy transition
- Spectrum unique for each atom and helps identify elements
- Lyman, Balmer, and Paschen series prominent for hydrogen atom
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Bohr Model of Atom-VI – Calculating Energy Levels
- Energy of an electron in nth orbit given by E = -13.6/n^2 eV
- Negative sign indicates the energy is bound and stable
- Energy difference between levels determines the wavelength/frequency of emitted/absorbed radiation
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Bohr Model of Atom-VII – Limitations
- Works only for hydrogen-like ions (single-electron systems)
- Does not explain relative intensities of spectral lines
- Neglects wave-particle duality and Heisenberg uncertainty principle
- Struggles to explain broadening of spectral lines
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Bohr Model of Atom-VIII – Significance
- Laid foundation for further quantum mechanical theories
- Explained hydrogen line spectrum that baffled scientists
- Led to development of more accurate quantum models
- Historical importance in the field of atomic structure
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Bohr Model of Atom-IX – Applications
- Understanding atomic structure and energy levels
- Explaining line spectra of elements
- Optical physics - lasers, fluorescence, and phosphorescence
- Basis for quantum mechanics and electron configuration
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Bohr Model of Atom-X – Conclusion
- Bohr’s model revolutionized the understanding of atomic structure
- Explained the stability and spectral lines of hydrogen atom
- Paved the way for the development of quantum mechanics
- Still serves as a useful conceptual model in certain applications
Bohr Model of Atom-XI – Electromagnetic Radiation
- Electromagnetic radiation: Form of energy that travels in waves
- Exhibits wave-particle duality (simultaneously behaves as waves and particles)
- Comprises oscillating electric and magnetic fields
- Characterized by wavelength (λ), frequency (ν), and speed of light (c)
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Bohr Model of Atom-XII – Wavelength and Frequency
- Wavelength (λ): Distance between two consecutive points on a wave (in meters)
- Frequency (ν): Number of wave cycles passing a point in one second (in hertz, Hz)
- Inversely related: λ = c/ν and ν = c/λ
- Different types of electromagnetic waves have different wavelengths and frequencies
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Bohr Model of Atom-XIII – Energy of a Photon
- Photons: Particles of light or electromagnetic radiation
- Energy of a photon (E) determined by its frequency
- Energy of a photon given by E = hν
- ‘h’ is Planck’s constant (6.63 x 10^-34 J·s), fundamental constant in quantum mechanics
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Bohr Model of Atom-XIV – Energy-Equivalent Equation
- Energy-equivalent equation relates energy, frequency, and wavelength
- E = hν = hc/λ
- ‘c’ is the speed of light (3.0 x 10^8 m/s)
- Allows energy to be expressed in various units (Joules, electron volts, etc.)
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Bohr Model of Atom-XV – Calculating Energy of a Photon
- Given the frequency (ν) or wavelength (λ), energy of a photon can be calculated
- Example 1: Calculate energy of a photon with a frequency of 5.0 x 10^14 Hz
- E = hν = (6.63 x 10^-34 J·s)(5.0 x 10^14 Hz)
- E = 3.3 x 10^-19 J (Joules)
- Example 2: Calculate energy of a photon with a wavelength of 600 nm
- Convert wavelength to meters: λ = 600 nm = 600 x 10^-9 m
- E = hc/λ = [(6.63 x 10^-34 J·s)(3.0 x 10^8 m/s)] / (600 x 10^-9 m)
- E = 3.31 x 10^-19 J (Joules)
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Bohr Model of Atom-XVI – Absorption and Emission Spectrum
- Absorption spectrum: When an atom absorbs specific wavelengths of light and leaves dark lines in the spectrum
- Emission spectrum: When an atom emits specific wavelengths of light and leaves bright lines in the spectrum
- Both absorption and emission spectra are unique for each element
Bohr Model of Atom-XVII – Balmer Series
- Balmer series: Emission lines in the visible spectrum of hydrogen atom
- Electrons transition from higher energy levels to n=2 energy level
- Wavelengths in Balmer series given by 1/λ = R(1/4 - 1/n^2), where R is the Rydberg constant (109,677 cm^-1)
- Example: Calculate the wavelength of the Balmer line when n=3
- 1/λ = R(1/4 - 1/3^2) = (109,677 cm^-1)(1/4 - 1/9)
- λ = 656.3 nm
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Bohr Model of Atom-XVIII – Lyman Series
- Lyman series: Emission lines in the ultraviolet spectrum of hydrogen atom
- Electrons transition from higher energy levels to n=1 energy level
- Wavelengths in Lyman series given by 1/λ = R(1 - 1/n^2)
- Example: Calculate the wavelength of the Lyman line when n=4
- 1/λ = R(1 - 1/4^2) = (109,677 cm^-1)(1 - 1/16)
- λ = 97.2 nm
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Bohr Model of Atom-XIX – Paschen Series
- Paschen series: Emission lines in the infrared spectrum of hydrogen atom
- Electrons transition from higher energy levels to n=3 energy level
- Wavelengths in Paschen series given by 1/λ = R(1/9 - 1/n^2)
- Example: Calculate the wavelength of the Paschen line when n=5
- 1/λ = R(1/9 - 1/5^2) = (109,677 cm^-1)(1/9 - 1/25)
- λ = 1875 nm
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Bohr Model of Atom-XX – Bohr’s Model and Modern Quantum Mechanics
- Bohr’s model laid the foundation for understanding atomic structure
- Modern quantum mechanics expanded on Bohr’s ideas
- Dual nature of electrons (wave-particle duality) explained by Schrödinger’s equation
- Electron cloud model and probability distributions replaced the concept of fixed orbits
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Bohr Model of Atom-XXI – Heisenberg Uncertainty Principle
- Heisenberg uncertainty principle: It is not possible to precisely measure the position and momentum of a particle simultaneously
- Limitations in knowledge of electron path in Bohr’s model resolved by the uncertainty principle
- Describes the fundamental limitations of measurement in quantum mechanics
Bohr Model of Atom-XXI – Heisenberg Uncertainty Principle
- Heisenberg uncertainty principle: It is not possible to precisely measure the position and momentum of a particle simultaneously
- Limitations in knowledge of electron path in Bohr’s model resolved by the uncertainty principle
- Describes the fundamental limitations of measurement in quantum mechanics
- Δx Δp ≥ h/4π
- Δx is the uncertainty in position
- Δp is the uncertainty in momentum
- h is Planck’s constant
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Bohr Model of Atom-XXII – Atomic Spectra
- Each element has a unique atomic spectrum
- Atomic spectra result from the arrangement of electrons in energy levels
- Ground state: Lowest energy state where electrons occupy the lowest energy levels
- Excited state: Higher energy state where electrons occupy higher energy levels
- Emission and absorption spectra provide information about the energy levels in an atom
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Bohr Model of Atom-XXIII – Quantum Numbers
- Quantum numbers describe the properties and characteristics of electrons in an atom
- Principal quantum number (n): Determines the energy level and size of the orbital (n = 1, 2, 3, …)
- Angular momentum quantum number (l): Determines the shape of the orbital (l = 0 to n-1)
- Magnetic quantum number (ml): Determines the orientation of the orbital (-l to +l)
- Spin quantum number (ms): Describes the spin direction of the electron (+1/2 or -1/2)
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Bohr Model of Atom-XXIV – Electron Configurations
- Electron configuration: Distribution of electrons among the energy levels and orbitals in an atom
- Follows the order of filling: 1s, 2s, 2p, 3s, 3p, …
- Aufbau principle: Electrons occupy the lowest energy level available
- Pauli exclusion principle: No two electrons in an atom can have the same set of quantum numbers
- Hund’s rule: Electrons occupy orbitals of the same energy level singly, with parallel spin, before pairing up
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Bohr Model of Atom-XXV – Orbital Diagrams
- Orbital diagrams represent the distribution of electrons in energy levels and orbitals
- Each box or line represents an orbital, with up and down arrows for electron spin
- Example: Oxygen (O) has atomic number 8
- Electron configuration: 1s^2 2s^2 2p^4
- Orbital diagram: 1s↓↑ 2s↓↑ 2p↑ ↑ ↑ ↑
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Bohr Model of Atom-XXVI – Valence Electrons
- Valence electrons: Electrons in the outermost energy level of an atom
- Determine the chemical properties and reactivity of an element
- Elements in the same group have the same number of valence electrons
- Example: Carbon (C) has atomic number 6 and electron configuration of 1s^2 2s^2 2p^2
- Carbon has 4 valence electrons
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Bohr Model of Atom-XXVII – Electron Dot Structures
- Electron dot structures (Lewis structures) represent valence electrons as dots around the chemical symbol
- Each dot represents one valence electron
- Example: Nitrogen (N) has atomic number 7 and electron configuration of 1s^2 2s^2 2p^3
- Electron dot structure: N: . .
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Bohr Model of Atom-XXVIII – Ionization Energy
- Ionization energy: Energy required to remove an electron from an atom or ion in the gas phase
- Trend: Ionization energy generally increases across a period and decreases down a group
- Atoms with low ionization energy are more likely to form cations (lose electrons)
- Example: Ionization energy of lithium (Li) is 520 kJ/mol
- Li(g) → Li^+(g) + e^- ΔH = 520 kJ/mol
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Bohr Model of Atom-XXIX – Electron Affinity
- Electron affinity: Energy change when an electron is added to an atom or ion in the gas phase
- Trend: Electron affinity generally increases across a period and decreases down a group
- Atoms with high electron affinity are more likely to form anions (gain electrons)
- Example: Electron affinity of chlorine (Cl) is -349 kJ/mol
- Cl(g) + e^- → Cl^-(g) ΔH = -349 kJ/mol
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Bohr Model of Atom-XXX – Summary
- Bohr’s model of the atom explained the stability and line spectra of hydrogen
- Energy levels in the Bohr model are quantized and determined by the principal quantum number (n)
- Electrons transition between energy levels by absorbing or emitting energy
- The Bohr model has limitations, but it laid the foundation for further developments in quantum mechanics
- Quantum numbers, electron configurations, and orbital diagrams are used to describe electron arrangement
- Valence electrons and electron dot structures are important for chemical bonding
- Ionization energy and electron affinity provide insights into the reactivity of elements