According to Planck's equation, the energy of a photon is directly proportional to its frequency. Planck's equation can be written as:
E = hf
Where: E is the energy of the photon, h is Planck's constant (a fundamental constant of nature), f is the frequency of the photon.
The speed of light (c) is also related to the wavelength (λ) and frequency (f) of a photon through the equation:
c = λf
Combining these equations, we can relate the energy of a photon to its wavelength:
E = hc/λ
This equation shows an inverse relationship between energy (E) and wavelength (λ). As the wavelength increases, the energy decreases, and vice versa.
When applied to the understanding of atomic structure and matter, Planck's equation provides insight into the quantized nature of energy. It suggests that energy is not continuous, but rather comes in discrete packets called "quanta" or "photons." The energy of each quantum is directly proportional to its frequency.
This understanding had profound implications for the development of quantum mechanics. It led to the concept of quantized energy levels in atoms and the notion that electrons occupy specific energy levels or orbitals. Electrons can absorb or emit energy only in discrete amounts corresponding to the difference in energy between these levels. The relationship between energy, wavelength, and frequency provided by Planck's equation forms the foundation of our understanding of atomic spectra, including the absorption and emission of light by atoms.
In summary, Planck's equation establishes the relationship between the energy, frequency, and wavelength of photons. It helps us understand the quantized nature of energy and forms the basis for our understanding of atomic structure and the behavior of matter at the microscopic level.