Understanding the Relationship
The relationship between the frequency (f) and wavelength (λ) of light is described by the following equation:
* c = fλ
where:
* c is the speed of light in a vacuum (approximately 3 x 10⁸ meters per second)
* f is the frequency of the light in Hertz (Hz)
* λ is the wavelength of the light in meters (m)
Calculation
1. Convert frequency to Hertz: The frequency given is 4.47 x 10¹⁴ Hz.
2. Rearrange the equation to solve for wavelength:
λ = c / f
3. Plug in the values:
λ = (3 x 10⁸ m/s) / (4.47 x 10¹⁴ Hz)
4. Calculate the wavelength:
λ ≈ 6.71 x 10⁻⁷ meters
Converting to Nanometers:
Wavelengths of light are often expressed in nanometers (nm). Since 1 meter = 10⁹ nanometers:
* 6.71 x 10⁻⁷ meters * (10⁹ nm / 1 meter) = 671 nm
Answer: The wavelength of light with a frequency of 4.47 x 10¹⁴ Hz is approximately 671 nanometers. This falls within the visible light spectrum, appearing as red light.
