Understanding the Relationship
The relationship between the wavelength (λ), frequency (ν), and the speed of light (c) is given by:
c = λν
* c: Speed of light in a vacuum (approximately 3 x 10⁸ m/s)
* λ: Wavelength (in meters)
* ν: Frequency (in Hertz, Hz)
Calculations
1. Rearrange the formula to solve for wavelength (λ):
λ = c / ν
2. Plug in the values:
λ = (3 x 10⁸ m/s) / (1.82 x 10¹⁸ Hz)
3. Calculate:
λ ≈ 1.65 x 10⁻¹⁰ meters
Conversion to Nanometers (nm)
Since wavelengths are often expressed in nanometers, let's convert:
* 1 meter = 10⁹ nanometers
* λ ≈ 1.65 x 10⁻¹⁰ meters * (10⁹ nm / 1 meter) = 165 nm
Answer
The wavelength of the electromagnetic wave with a frequency of 1.82 x 10¹⁸ Hz in a vacuum is approximately 165 nanometers.
