Understanding the Relationship
The relationship between the wavelength (λ), frequency (ν), and the speed of light (c) is given by the following equation:
* c = λν
Where:
* c is the speed of light (approximately 3 x 10⁸ m/s)
* λ is the wavelength (in meters)
* ν is the frequency (in Hertz, Hz)
Calculation
1. Rearrange the equation to solve for wavelength (λ):
λ = c / ν
2. Plug in the values:
λ = (3 x 10⁸ m/s) / (7.81 x 10¹⁴ Hz)
3. Calculate the result:
λ ≈ 3.84 x 10⁻⁷ m
Converting to Nanometers (nm)
Since wavelengths are often expressed in nanometers, you can convert the answer:
* 1 meter (m) = 1 x 10⁹ nanometers (nm)
Therefore:
* λ ≈ 3.84 x 10⁻⁷ m * (1 x 10⁹ nm/m) = 384 nm
Answer: The wavelength of a photon with a frequency of 7.81 x 10¹⁴ Hz is approximately 384 nm.
