How did Plank explain the black body radiation?

Black body radiation refers to the radiation emitted by a perfect absorber and emitter of electromagnetic radiation, called a "black body." The spectrum of radiation emitted by a black body depends only on its temperature and is characterized by a distribution of wavelengths.
Before Planck, classical physics, particularly the Rayleigh-Jeans Law, could not explain the observed behavior of black body radiation, especially at short wavelengths (the so-called "ultraviolet catastrophe"). Planck's theory, developed in 1900, resolved this issue.
Planck's Explanation:
1. Quantization of Energy: Planck proposed that the energy of the oscillators (or particles) that emitted radiation inside the black body cavity was not continuous, but rather quantized. This means that energy could only be emitted or absorbed in discrete amounts, or "quanta." The energy of each quantum was given by the equation:
E=hνE = h \nu
where:
o EE is the energy of the quantum,
o hh is Planck's constant (h=6.626×10−34 J\cdotpsh = 6.626 \times 10^{-34} \, \text{J·s}),
o ν\nu is the frequency of the radiation.
2. Planck's Law: Using this concept of quantized energy, Planck derived an equation for the spectral distribution of black body radiation:
B(ν,T)=8πhν3c3⋅1ehνkT−1B(\nu, T) = \frac{8 \pi h \nu^3}{c^3} \cdot \frac{1}{e^{\frac{h \nu}{kT}} - 1}
where:
o B(ν,T)B(\nu, T) is the energy radiated per unit frequency,
o ν\nu is the frequency of the radiation,
o TT is the temperature of the black body,
o hh is Planck's constant,
o kk is the Boltzmann constant,
o cc is the speed of light.
3. Key Ideas in Planck’s Theory:
o The quantization of energy was a revolutionary idea, and it resolved the paradox of the ultraviolet catastrophe.
o Planck's law showed that the intensity of radiation increases with temperature and follows a specific curve, with the peak of the curve shifting to shorter wavelengths as the temperature increases.
Impact:
Planck's work laid the foundation for quantum mechanics, influencing later developments such as Einstein's work on the photoelectric effect and the establishment of quantum theory. It provided a theoretical explanation for black body radiation and marked the birth of quantum theory.
Final Answer:
Planck explained black body radiation by introducing the concept of quantized energy levels for the oscillators within the black body and deriving the Planck law for the radiation spectrum, which successfully explained the observed distribution of radiation without leading to the ultraviolet catastrophe.