Understanding the Relationship
The relationship between the frequency (f) of light, its wavelength (λ), and the speed of light (c) is given by:
c = fλ
Where:
* c is the speed of light in a vacuum (approximately 3 x 10⁸ m/s)
* f is the frequency in Hertz (Hz)
* λ is the wavelength in meters (m)
Calculation
1. Rearrange the equation to solve for wavelength:
λ = c / f
2. Plug in the values:
λ = (3 x 10⁸ m/s) / (7.21 x 10¹⁴ Hz)
3. Calculate:
λ ≈ 4.16 x 10⁻⁷ m
Converting to Nanometers
Since wavelengths of light are often expressed in nanometers (nm), let's convert our answer:
* 1 meter (m) = 10⁹ nanometers (nm)
* λ ≈ 4.16 x 10⁻⁷ m * (10⁹ nm/m)
* λ ≈ 416 nm
Therefore, the wavelength of a light frequency of 7.21 x 10¹⁴ Hz is approximately 416 nm.
