Question

Assume the speed of light to be 3×10^8 m/s. If the frequency of an electromagnetic wave is 500,000 GHz (GHz=gigahertz=10^9m/s), what is the wavelength of that radiation in micrometers?

Answer 1

To find the wavelength of the electromagnetic wave, we can use the formula:

Wavelength = Speed of Light / Frequency

Given: Speed of Light = 3 × 10^8 m/s Frequency = 500,000 GHz = 500,000 × 10^9 Hz

Let's calculate the wavelength:

Wavelength = (3 × 10^8 m/s) / (500,000 × 10^9 Hz)

Converting GHz to Hz: Wavelength = (3 × 10^8 m/s) / (500,000 × 10^9 Hz) = (3 × 10^8 m/s) / (500 × 10^12 Hz) = (3/500) × 10^-4 m

Converting meters to micrometers (µm): Wavelength = (3/500) × 10^-4 m × (10^6 µm/1 m) = (3/500) × 10^2 µm

Wavelength = 0.006 µm

Therefore, the wavelength of the electromagnetic wave with a frequency of 500,000 GHz is approximately 0.006 micrometers (µm).