Wave Nature of EMR:
- EMR travels in waves and has associated properties like wavelength ($\lambda$), frequency ($\nu$), and speed ($c$).
- Relationship: $c = \lambda \nu$, where $c = 3.0 \times 10^8 \text{ m/s}$ (speed of light in vacuum).
- Units: $\lambda$ in meters (m), nanometers (nm), Ångstroms (Å); $\nu$ in hertz (Hz or s$^{-1}$).
Particle Nature of EMR (Planck's Quantum Theory):
- EMR is emitted or absorbed in discrete packets of energy called quanta or photons.
- Energy of a single photon: $E = h\nu = \frac{hc}{\lambda}$
- $h$ (Planck's constant) = $6.626 \times 10^{-34} \text{ Js}$.
Photoelectric Effect:
- The phenomenon of ejection of electrons from the surface of a metal when light of suitable frequency (above a certain threshold) strikes it.
- Key Observations:
  - Electrons are ejected only if the incident light has frequency greater than a certain minimum frequency, $\nu_0$ (threshold frequency).
  - The number of ejected electrons is proportional to the intensity of incident light.
  - The kinetic energy of the ejected electrons is directly proportional to the frequency of incident light (above $\nu_0$).
  - There is no time lag between the incidence of light and the ejection of electrons.
- Einstein's Equation: $h\nu = h\nu_0 + KE_{max}$ or $h\nu = W_0 + \frac{1}{2}mv^2$

Postulates:
1. Electrons revolve around the nucleus in specific, stable circular paths called orbits or stationary states. Each orbit has a fixed radius and energy.
2. Electrons in these stationary orbits do not radiate energy.
3. The angular momentum of an electron in a given orbit is quantized, meaning it can only take certain discrete values: $mvr = n\frac{h}{2\pi}$, where $n = 1, 2, 3, ...$ (principal quantum number).
4. Energy is absorbed or emitted only when an electron jumps from one stationary orbit to another.
  - Absorption: Electron moves from a lower to a higher energy orbit.
  - Emission: Electron moves from a higher to a lower energy orbit.
  The energy difference is given by $\Delta E = E_{final} - E_{initial} = h\nu$.

Radius of $n^{th}$ orbit ($r_n$): $r_n = 0.529 \times \frac{n^2}{Z} \text{ Å}$
- $n$: principal quantum number ($1, 2, 3, ...$)
- $Z$: atomic number (for H, $Z=1$; for He$^+$, $Z=2$; for Li$^{2+}$, $Z=3$)
- $r_1$ for H-atom (Bohr radius) $\approx 0.529 \text{ Å}$
Energy of $n^{th}$ orbit ($E_n$):
- $E_n = -13.6 \times \frac{Z^2}{n^2} \text{ eV/atom}$
- $E_n = -2.18 \times 10^{-18} \times \frac{Z^2}{n^2} \text{ J/atom}$
- The negative sign indicates that the electron is bound to the nucleus. As $n$ increases, energy becomes less negative (i.e., increases).
Velocity of electron in $n^{th}$ orbi