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
* c: Speed of light in a vacuum, approximately 3.00 x 10⁸ m/s
* λ: Wavelength (in meters)
* ν: Frequency (in Hertz, or s⁻¹)
Calculation
1. Rearrange the equation to solve for wavelength:
λ = c / ν
2. Plug in the values:
λ = (3.00 x 10⁸ m/s) / (7.7 x 10¹⁰ s⁻¹)
3. Calculate the wavelength:
λ ≈ 3.89 x 10⁻³ m
Converting to a more convenient unit:
Since the wavelength is very small, it's often more convenient to express it in millimeters (mm):
λ ≈ 3.89 x 10⁻³ m * (1000 mm / 1 m) ≈ 3.89 mm
Therefore, the wavelength of radiation with a frequency of 7.7 x 10¹⁰ s⁻¹ is approximately 3.89 mm.
