Electrons in Atoms - Part 1 Summary

Electromagnetic radiation is the emission and transmission of energy in waves.
$c = λν$ where $c$ is the speed of light ( $3.00 \times 10^8$ m/s in vacuum), $λ$ is wavelength, and $ν$ is frequency.
Molecules interact with electromagnetic radiation through rotation (microwave), vibration (IR), translation (across spectrum), and electronic transition (UV).
Planck's equation: $E = hν$ , where $h$ is Planck's constant ( $6.626 \times 10^{-34} \text{ J s}$ ).

Atomic emission spectrum: Gas emits light when an electric current passes through it.
Absorption spectrum: White light passes through a gas, showing absorbed wavelengths.
Each element has a unique spectrum, useful for identification.
Rydberg equation: $\frac{1}{λ} = R<em>H \left( \frac{1}{n</em>1^2} - \frac{1}{n_2^2} \right)$ , relates wavelengths in the hydrogen spectrum.
Bohr's postulates:
- Electrons exist in discrete energy levels without emitting radiation.
- Electrons can move between energy levels, emitting or absorbing monochromatic radiation: $\Delta E = hν$ .
- Electron's angular momentum is quantized: $mvr = \frac{nh}{2π}$ .
Bohr's theory correctly explains the H emission spectrum but fails for other elements.

Ionization energy is the energy to remove an electron from an atom.
For hydrogen-like species: $E<em>n = -Z^2 \frac{R</em>H}{n^2}$ ; where $Z$ is the atomic number

Light has both wave and particle nature.
Einstein's explanation: $hν = KE + W$ , where $KE$ is kinetic energy of ejected electron and $W$ is the work function.
If hν > W, electrons are ejected; otherwise, they aren't.

De Broglie relationship: $λ = \frac{h}{mv}$ , where $λ$ is the wavelength of a particle.
Electrons exhibit wave-particle duality, verified by Davisson & Germer.