Electromagnetic Radiation and Atomic Spectra

Electromagnetic Radiations

  • Wave Properties
    • Wavelength (λ): Distance between two successive crests or troughs, measured in nanometers (1 nm = $10^{-9}$ m).
    • Frequency (v): Number of wave cycles passing a point in a unit time, measured in hertz (Hz).
  • Relationship:
    • Low frequency → Long wavelength
    • High frequency → Short wavelength

Atomic Spectra

  • Types of Radiation:
    • Monochromatic: Single wavelength.
    • Polychromatic: More than one wavelength.
  • Spectra: Result of separating polychromatic radiation into its constituent wavelengths.
    • Continuous Spectra: Wavelengths appear continuously (e.g., rainbow).
    • Line Spectra: Contains specific wavelengths only.

Bohr's Postulates

  • Electrons occupy only certain allowed orbits/radii corresponding to definite energies.
  • Allowed energy states do not radiate energy and do not spiral into the nucleus.
  • Energy is emitted/absorbed when electrons transition between allowed states, as photons:
    • $E = hv$

Energy Transitions

  • Emission: Electron falls from a higher energy level (nhi) to a lower (n).
    • Greater fall results in more energy emitted.
  • Absorption: Electron moves from a lower energy level (n₁) to a higher (n).
    • Greater jump results in more energy absorbed.

Energy Levels and Rydberg Formula

  • Energy of electron:
    • $En = -\frac{RH}{n^2}$
    • Where $R_H = 2.180 \times 10^{-18}$ J.
  • Principal quantum number (n):
    • Possible values: 1, 2, 3,…
  • Energy States:
    • Zero energy: Proton and electron infinitely separated.
    • Negative energy states correspond to all states below zero.
    • Ground state: Lowest energy (n = 1).
    • Excited states: n values above 1.