Planck's quantum theory, also known as quantum mechanics, provides a mathematical framework to describe the behavior of particles at the microscopic level. One of its key principles is the idea that energy is quantized, meaning it can only exist in discrete amounts or "quanta."
When applied to electromagnetic radiation, such as light, Planck's theory explains the relationship between wavelength and intensity through the concept of photons. According to the theory, light can be thought of as a stream of particles called photons, each carrying a specific amount of energy. The energy of a photon is directly proportional to its frequency, which is inversely proportional to its wavelength.
The energy of a photon can be calculated using the equation E = hf, where E is the energy, h is Planck's constant (a fundamental constant in quantum mechanics), and f is the frequency of the radiation. Since the speed of light is a constant, the frequency and wavelength of light are inversely related by the equation c = λf, where c is the speed of light and λ is the wavelength.
Combining these two equations, we have E = hf = hc/λ, where λ is the wavelength. This equation demonstrates that the energy of a photon is inversely proportional to its wavelength. In other words, photons with shorter wavelengths have higher energy, while photons with longer wavelengths have lower energy.
The intensity of light refers to the amount of energy carried by a beam of light per unit area per unit time. It is related to the number of photons hitting a surface within a given time interval. Since the energy of each photon is inversely proportional to its wavelength, the total energy carried by photons of different wavelengths (or frequencies) will be distributed differently.
In the case of a continuous spectrum of light, such as that emitted by a blackbody radiator, the distribution of photons with different energies (or wavelengths) follows Planck's law. Planck's law describes the intensity of radiation at different wavelengths as a function of temperature, and it precisely matches the experimental observations of blackbody radiation.
The graph of a wavelength-intensity relationship, known as the spectral distribution curve, illustrates the intensity of radiation at different wavelengths. In the context of Planck's theory, this curve represents the distribution of photons of different energies (or wavelengths) in the emitted radiation.
Planck's quantum theory, with its concept of quantized energy and the idea that photons carry discrete amounts of energy, provides a theoretical foundation that accurately explains the relationship between wavelength and intensity observed in experiments and matches the spectral distribution curves associated with different sources of radiation.