Understanding the Relationship

The relationship between the speed of light (c), frequency (f), and wavelength (λ) is given by:

c = fλ

Where:

* c is the speed of light (approximately 3 x 10^8 meters per second)

* f is the frequency (in Hertz, Hz)

* λ is the wavelength (in meters)

Calculation

1. Rearrange the formula to solve for wavelength:

λ = c / f

2. Plug in the values:

λ = (3 x 10^8 m/s) / (4.6 x 10^12 Hz)

3. Calculate:

λ ≈ 6.52 x 10^-5 meters

Conversion to Micrometers (µm)

Since wavelengths in this range are often expressed in micrometers, let's convert:

6.52 x 10^-5 meters * (10^6 µm / 1 meter) = 65.2 µm

Answer: The wavelength of light with a frequency of 4.6 x 10^12 Hz is approximately 65.2 µm.