7.1 Quantum Theory of Light
1. Blackbody Radiation and Quantum Concept
A blackbody is an ideal absorber and emitter of electromagnetic radiation across all wavelengths. Classical wave theory failed to explain blackbody radiation spectrum curves at short wavelengths (the Ultraviolet Catastrophe).
2. Quantum Energy of Light (Max Planck & Albert Einstein)
Max Planck proposed that light energy is emitted in discrete packets of energy called quanta or photons. The energy of a single photon ($E$) is directly proportional to its frequency ($f$):
$$E = h f = h \frac{c}{\lambda}$$
- $E$ = Energy of a single photon ($\text{J}$)
- $h$ = Planck's constant ($6.63 \times 10^{-34}\text{ J s}$)
- $f$ = Frequency of light ($\text{Hz}$)
- $c$ = Speed of light in vacuum ($3.0 \times 10^8\text{ m s}^{-1}$)
- $\lambda$ = Wavelength of light ($\text{m}$)
3. Wave-Particle Duality and de Broglie Wavelength
Louis de Broglie hypothesized that subatomic particles with momentum ($p = mv$) also exhibit wave properties. The de Broglie wavelength ($\lambda$) of a particle is given by:
$$\lambda = \frac{h}{p} = \frac{h}{m v}$$
7.2 Photoelectric Effect
1. Concept of Photoelectric Effect
The photoelectric effect is the emission of electrons (photoelectrons) from a metal surface when illuminated by light of a sufficiently high frequency.
2. Key Characteristics of Photoelectric Effect
- Emission occurs only if light frequency $f \ge f_0$ (threshold frequency).
- Emission occurs instantaneously without any time delay.
- Maximum kinetic energy ($K_{\text{max}}$) of emitted photoelectrons depends solely on frequency $f$, not on light intensity.
- Light intensity controls only the rate of photon arrival (number of photoelectrons emitted per second).
7.3 Einstein's Photoelectric Theory
1. Einstein's Photoelectric Equation
According to Albert Einstein, the photon energy ($E = hf$) absorbed by an electron in a metal is divided into two parts:
- Work function ($\Phi = h f_0$): Minimum energy required to free the electron from the metal surface.
- Maximum kinetic energy ($K_{\text{max}} = \frac{1}{2} m v_{\text{max}}^2$): Remaining energy converted to electron motion.
$$E = \Phi + K_{\text{max}} \implies h f = h f_0 + \frac{1}{2} m v_{\text{max}}^2$$
2. Stopping Potential ($V_s$)
The stopping potential ($V_s$) is the minimum negative potential applied to the anode that completely stops the fastest photoelectrons from reaching it:
$$K_{\text{max}} = e V_s \implies e V_s = h f - h f_0$$
- $e$ = Charge of an electron ($1.6 \times 10^{-19}\text{ C}$)
- $V_s$ = Stopping potential ($\text{V}$)
3. Applications of Photoelectric Effect
- Solar Cells (Photovoltaic): Converts light energy directly into electrical current in satellites and calculators.
- Light Sensors / Dusk-to-Dawn Switches: Automatically switches on outdoor lights when ambient sunlight drops.
- Photocell in Security Alarms: Triggers an alarm when an invisible light beam is broken by an intruder.