Understanding the Relationship
The speed of light (c) is related to the frequency (f) and wavelength (λ) of an electromagnetic wave by the following equation:
c = fλ
Solving for Wavelength
1. Know the Speed of Light: The speed of light in a vacuum is approximately c = 3 x 10⁸ m/s.
2. Rearrange the Equation: To solve for wavelength, we need to rearrange the equation:
λ = c / f
3. Substitute the Values:
* c = 3 x 10⁸ m/s
* f = 1.82 x 10¹⁸ Hz
λ = (3 x 10⁸ m/s) / (1.82 x 10¹⁸ Hz)
4. Calculate:
λ ≈ 1.65 x 10⁻¹⁰ m
Converting to Nanometers:
Since wavelengths are often expressed in nanometers (nm), let's convert our answer:
1.65 x 10⁻¹⁰ m * (10⁹ nm / 1 m) = 165 nm
Answer: The wavelength of the electromagnetic wave is approximately 165 nm.
