Understanding the Relationship
The relationship between the wavelength (λ) of light, its frequency (ν), and the speed of light (c) is given by the following equation:
* c = λν
Where:
* c is the speed of light in a vacuum (approximately 3 x 10⁸ meters per second)
* λ is the wavelength (in meters)
* ν is the frequency (in Hertz, Hz)
Calculations
1. Rearrange the equation to solve for wavelength:
λ = c / ν
2. Plug in the values:
λ = (3 x 10⁸ m/s) / (6.42 x 10¹⁴ Hz)
3. Calculate the wavelength:
λ ≈ 4.67 x 10⁻⁷ meters
Converting to Nanometers
Since wavelengths are often expressed in nanometers (nm), let's convert the answer:
* 1 meter = 10⁹ nanometers
* λ ≈ 4.67 x 10⁻⁷ meters * (10⁹ nm / 1 meter)
* λ ≈ 467 nm
Answer:
The wavelength of light with a frequency of 6.42 x 10¹⁴ Hz is approximately 467 nanometers.
