Final answer:
To find the wavelength (λ) of the photon, with a frequency of 4.2 x 10^14 Hz, divide the speed of light (c) by the frequency (f). We get λ = (3.00 x 10^8 m/s) / (4.2 x 10^14 Hz), which calculates to approximately 714 nanometers.
Step-by-step explanation:
To calculate the wavelength of a photon with a frequency of 4.2 x 1014 Hz, we use the following formula:
c = λ x f
Where:
- c is the speed of light (3.00 x 108 m/s)
- λ (lambda) is the wavelength we want to find
- f is the frequency (4.2 x 1014 Hz)
Rearranging the formula to solve for λ gives us:
λ = c / f
Substituting the known values:
λ = (3.00 x 108 m/s) / (4.2 x 1014 Hz)
Performing the calculation provides:
λ = 7.14 x 10-7 meters, which is 714 nm (nanometers).
The wavelength of the photon is therefore approximately 714 nanometers.