The energy of a photon is directly related to its frequency, described by the equation E = hv, where E is the energy, h is Planck’s constant, and v is the frequency of the light. Additionally, the frequency and wavelength (λ) of light are connected by the equation v = c / λ, where c is the speed of light (approximately 2.998 x 108 m/s).
To further break this down, when you know the wavelength of light, you can find its frequency by rearranging the second equation: v = c / λ. For instance, if light has a wavelength of 500 nm (which is 5 x 10-7 m), you can substitute it into the equation to find its frequency:
v = c / λ = (2.998 x 108 m/s) / (5 x 10-7 m) = 5.996 x 1014 Hz
Once you have the frequency, you can calculate the energy of the photon using the first equation:
E = hv = (6.626 x 10-34 J·s) x (5.996 x 1014 Hz) = 3.97 x 10-19 J
This illustrates how the energy of a photon increases with higher frequency (or shorter wavelength). In summary, the relationships among energy, frequency, and wavelength are fundamental principles in understanding light and electromagnetic radiation.