The Inverse Relationship: Energy and Wavelength
A photon's energy is inversely proportional to its wavelength. This means that as the wavelength of a photon increases, its energy decreases, and conversely, as its wavelength decreases, its energy increases. This fundamental relationship is described by Planck's equation, E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ (lambda) is the wavelength.
Key Principles: Planck's Constant and Speed of Light
The constants in the equation, Planck's constant (h ≈ 6.626 x 10^-34 J·s) and the speed of light (c ≈ 3 x 10^8 m/s), highlight the quantum nature of light. Planck's constant quantifies the relationship between the energy of a photon and its frequency, while the speed of light connects wavelength and frequency (c = λv, where v is frequency). Together, they establish the precise mathematical link between a photon's wave-like property (wavelength) and its particle-like property (energy).
A Practical Example: Visible Light Spectrum
Consider the visible light spectrum. Violet light has a shorter wavelength (around 400 nm) and therefore higher energy per photon compared to red light, which has a longer wavelength (around 700 nm) and lower energy per photon. This is why ultraviolet (UV) light, with even shorter wavelengths than violet, carries enough energy to damage skin cells and DNA, while infrared (IR) light, with longer wavelengths than red, is primarily associated with heat without causing such damage.
Importance in Science and Technology
This relationship is crucial across many scientific fields. In astronomy, it allows scientists to determine the temperature and composition of distant stars by analyzing the wavelengths of light they emit. In medical imaging, techniques like X-rays (short wavelength, high energy) are used for internal scans, while MRI uses radio waves (long wavelength, low energy) to create detailed images. It is also foundational to technologies like lasers, solar cells, and spectroscopy, which analyze material properties based on their interaction with specific light wavelengths.