Understanding the Relationship
The relationship between the frequency (f) of light and its wavelength (λ) 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 in Hertz (Hz)
* λ is the wavelength in meters
Calculations
1. Rearrange the equation to solve for wavelength:
λ = c / f
2. Plug in the given values:
λ = (3 x 10⁸ m/s) / (7.21 x 10¹⁴ Hz)
3. Calculate the wavelength:
λ ≈ 4.16 x 10⁻⁷ meters
Converting to Nanometers
Wavelength is often expressed in nanometers (nm). Since 1 meter = 1 x 10⁹ nanometers, we can convert the wavelength:
λ ≈ 4.16 x 10⁻⁷ meters * (1 x 10⁹ nm / 1 meter)
λ ≈ 416 nm
Answer:
The wavelength of light with a frequency of 7.21 x 10¹⁴ Hz is approximately 416 nanometers.
