Planck’s quantum theory, black-body radiation

1. Introduction to Quantum Physics

1. Quantum physics is the study of phenomena at atomic and subatomic levels.
2. Revolutionized classical physics by introducing the concept of quantization.
3. Developed to explain phenomena that could not be explained by classical theories.

2. Planck’s Quantum Theory

1. Proposed by Max Planck in 1900 to explain black-body radiation.
2. Energy is emitted or absorbed in discrete packets called quanta or photons.
3. The energy of each quantum is proportional to its frequency, given by E = hν, where:
   • E is the energy of the quantum.
   • h is Planck's constant (6.626 × 10⁻³⁴ Js).
   • ν is the frequency of the radiation.
4. Introduced the idea of energy quantization, a cornerstone of quantum mechanics.

3. Black-Body Radiation

1. A black body is an idealized object that absorbs all incident radiation and emits radiation at all wavelengths.
2. Classical physics failed to explain the observed spectrum of black-body radiation, known as the ultraviolet catastrophe.
3. Planck’s quantum theory successfully explained the spectrum of black-body radiation.
4. The intensity of radiation emitted by a black body depends on its temperature and wavelength.
5. Key laws related to black-body radiation:
   • Wien’s Displacement Law: The peak wavelength of radiation is inversely proportional to the temperature.
   • Stefan-Boltzmann Law: The total energy radiated per unit surface area is proportional to the fourth power of temperature.

4. Applications of Planck’s Quantum Theory

1. Explains phenomena like the photoelectric effect and atomic spectra.
2. Forms the basis for quantum mechanics and the study of subatomic particles.
3. Used in technologies such as lasers, LEDs, and solar cells.
4. Key in understanding the behavior of semiconductors and quantum computing.

5. Key Features of Black-Body Radiation

1. Intensity of emitted radiation increases with temperature.
2. The peak of the emission spectrum shifts to shorter wavelengths as temperature increases.
3. Explains the cosmic microwave background radiation, a remnant of the Big Bang.

6. Significance of Quantum Theory

1. Marked the beginning of the quantum revolution in physics.
2. Challenged the assumptions of classical physics.
3. Provided insights into the dual nature of light and matter.

7. Important Constants and Values

1. Planck's Constant: 6.626 × 10⁻³⁴ Js.
2. Speed of light (c): 3 × 10⁸ m/s.