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