Understanding the Relationship
The relationship between the frequency (f) of a photon, its wavelength (λ), and the speed of light (c) is described by the following equation:
* c = fλ
Where:
* c is the speed of light (approximately 3.00 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 = (3.00 x 10⁸ m/s) / (6.90 x 10¹⁴ Hz)
3. Calculate the result:
λ ≈ 4.35 x 10⁻⁷ m
Converting to Nanometers (nm)
Since wavelengths are often expressed in nanometers, you can convert the result:
* 4.35 x 10⁻⁷ m * (10⁹ nm / 1 m) = 435 nm
Answer:
The wavelength of a photon with a frequency of 6.90 x 10¹⁴ Hz is approximately 435 nanometers (nm).
