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} = RH \left( \frac{1}{n1^2} - \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: En = -Z^2 \frac{RH}{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.