Understanding the Relationship
The relationship between the frequency (ν) and wavelength (λ) of light is described by the following equation:
* c = νλ
where:
* c is the speed of light in a vacuum (approximately 3 x 10⁸ m/s)
* ν is the frequency in Hertz (Hz)
* λ is the wavelength in meters (m)
Calculation
1. Rearrange the equation to solve for wavelength:
λ = c / ν
2. Plug in the values:
λ = (3 x 10⁸ m/s) / (6.56 x 10¹⁴ Hz)
3. Calculate the wavelength:
λ ≈ 4.57 x 10⁻⁷ m
Converting to Nanometers (nm)
Since wavelengths are often expressed in nanometers, we can convert our answer:
* 1 meter (m) = 10⁹ nanometers (nm)
* λ ≈ 4.57 x 10⁻⁷ m * (10⁹ nm/m) = 457 nm
Therefore, the wavelength of a photon with a frequency of 6.56 x 10¹⁴ Hz is approximately 457 nm.
