What is the relationship between the frequency of a light wave and its energy and the relationship between the wavelength of a light wave and it's energy?
The energy of a light wave is directly proportional to its frequency and inversely proportional to its wavelength. This relationship is described by the equation:
Energy = Planck's constant × Frequency = (Planck's constant × speed of light) ÷ Wavelength
Here, Planck's constant is a fundamental constant in physics, denoted by the symbol "h," and the speed of light is denoted by "c." The unit of energy is typically measured in electron volts (eV) or joules (J). Frequency is measured in hertz (Hz), and wavelength is measured in meters (m).
In summary,
- Higher frequency light waves have higher energy.
- Lower wavelength light waves have higher energy.
The relationship between the frequency of a light wave and its energy is described by Planck's equation:
E = h * f
Where:
- E represents the energy of the light wave
- h is Planck's constant (approximately 6.63 x 10^-34 joule-seconds)
- f is the frequency of the light wave
According to this equation, the energy of a light wave is directly proportional to its frequency. In simpler terms, as the frequency increases, the energy also increases, and vice versa.
On the other hand, the relationship between the wavelength of a light wave and its energy can be derived using the speed of light, denoted as c. The speed of light is approximately 3 x 10^8 meters per second.
The equation that relates the wavelength, frequency, and speed of light is:
c = λ * f
Where:
- c is the speed of light
- λ represents the wavelength of the light wave
- f is the frequency of the light wave
Rearranging the equation, we get:
f = c / λ
Using the relationship between frequency and energy stated earlier, we can substitute f in Planck's equation:
E = h * (c / λ)
This equation shows that the energy of a light wave is inversely proportional to its wavelength. In other words, as the wavelength increases, the energy decreases, and vice versa.
So, to summarize:
- The frequency and energy of a light wave are directly proportional.
- The wavelength and energy of a light wave are inversely proportional.