Understanding the Relationship
The relationship between the frequency (f) of a photon 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 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 x 10⁸ m/s) / (4.72 x 10¹⁴ Hz)
3. Calculate:
λ ≈ 6.36 x 10⁻⁷ m
Converting to Nanometers
Since wavelengths are often expressed in nanometers (nm), we can convert the answer:
* 1 meter (m) = 1 x 10⁹ nanometers (nm)
* λ ≈ 6.36 x 10⁻⁷ m * (1 x 10⁹ nm / 1 m)
* λ ≈ 636 nm
Answer: The wavelength of a photon with a frequency of 4.72 x 10¹⁴ Hz is approximately 636 nm.
