Electromagnetic Spectrum & Bohr Atomic Model Notes

Module 7: Electromagnetic Spectrum & Bohr Atomic Model

Electromagnetic Radiation

• Definition: A method by which energy travels through space.
• Three Characteristics:
  • Wavelength (λ): Distance between two peaks or troughs in a wave.
  • Frequency (ν): Number of waves (cycles) passing a given point per second.
  • Speed (c): Speed of light, approximately $c = 2.9979 imes 10^{8} ext{ m/s}$.

Key Concepts of Wavelength and Frequency

• Wavelength (λ): Measured in nanometers (nm) or meters (m).
• Frequency (ν): Can be calculated using the formula:
  $<br />\nu = \frac{c}{λ}$
  Example: For a wavelength of $7.80 \times 10^{2} ext{ nm}$, the frequency is found to be $3.84 \times 10^{14} ext{ s}^{-1}$.

Energy and Photons

• Energy of a Photon: Calculated using the relationship:
  $E = h<br />\nu$
  where h = Planck's constant = $6.626 \times 10^{-34} ext{ J s}$.
• Key Idea: Energy can only be gained or lost in packets called quanta. Electromagnetic radiation consists of a stream of particles called photons.

Line vs Continuous Spectrum

• Continuous Spectrum: Contains all wavelengths of visible light, seen when white light is passed through a prism.
• Line Spectrum: Composed of discrete wavelengths corresponding to specific energy transitions in atoms, e.g., hydrogen and mercury spectra.

Energy Levels and Transitions

• Energy Levels (n): Electrons are arranged in defined energy levels, from n=1 (lowest) to higher levels.
• Energy Level Transitions:
  • An electron can absorb energy to jump to a higher level or emit energy (as a photon) to fall back to a lower level.
  • Example: Transition from n = 3 to n = 2 emits a photon with energy corresponding to the energy difference.

Bohr Model of the Atom

• Definition: Describes the atom with electrons orbiting in fixed paths (orbits) around the nucleus.
• Important Points:
  • Ground state = lowest energy state (n = 1).
  • Energy levels represent fixed distances from the nucleus.
  • The model works for hydrogen but is insufficient for multi-electron systems.

Quantum Mechanical Model

• Heisenberg Uncertainty Principle: States that one cannot simultaneously know both the exact position and momentum of an electron.
  $\Delta x \, \Delta (mv) \geq \frac{h}{4\pi}$
• Quantum Numbers:
  1. Principal Quantum Number (n): Indicates the size and energy of orbitals.
  2. Angular Momentum Quantum Number (l): Shape of orbitals (values from 0 to n-1).
  3. Magnetic Quantum Number (mₗ): Orientation of orbitals.
  4. Electron Spin Quantum Number (mₛ): Can be +1/2 or -1/2, related to the Pauli exclusion principle.

Chemical Properties and Valence Electrons

• Valence Electrons: Electrons in outermost principal energy level affecting the atom’s chemical properties.
  • Ultrahigh significance in determining bonding and reactivity.
• Example of Valence Electrons Distribution:
  • Oxygen (O): $1s^2 2s^2 2p^4$ → 6 valence electrons.

Periodic Trends

• Atomic Radius: Distance from nucleus to valence electrons.
  • Increases down a group; decreases across a period.
• Ionization Energy: Energy required to remove an electron; generally increases across a period and decreases down a group.
• Electron Affinity: Energy change upon adding an electron; generally increases from left to right across a period.

Summary of Learning Checks

• Several problems with calculations of frequency and energy for specific wavelengths.
• Use relationships between frequency (ν), wavelength (λ), and energy (E) to solve various scenarios regarding photon emissions and electronic transitions within the atomic structure.