Understanding the Relationship
* Frequency (ν) is how many wave cycles pass a point in one second (measured in Hertz, Hz, or s⁻¹).
* Wavelength (λ) is the distance between two consecutive crests or troughs of a wave (measured in meters, m).
* Speed of light (c) is a constant value (approximately 3 x 10⁸ m/s).
The relationship between these is:
c = λν
Solving for Wavelength
1. Rearrange the equation to solve for wavelength (λ):
λ = c / ν
2. Plug in the values:
λ = (3 x 10⁸ m/s) / (6.66 x 10¹⁴ s⁻¹)
3. Calculate the wavelength:
λ ≈ 4.5 x 10⁻⁷ m
Converting to Nanometers (nm)
Since wavelengths in the visible light spectrum are often expressed in nanometers, you can convert the answer:
1 nanometer (nm) = 1 x 10⁻⁹ meters (m)
Therefore:
λ ≈ 4.5 x 10⁻⁷ m * (1 nm / 1 x 10⁻⁹ m)
λ ≈ 450 nm
Conclusion
The wavelength of electromagnetic radiation with a frequency of 6.66 x 10¹⁴ s⁻¹ is approximately 450 nanometers. This falls within the visible light spectrum, specifically in the blue-green region.
