To calculate the wavelength of the electromagnetic wave, we can use the formula:
wavelength = speed of light / frequency
Given that the speed of light is 3 × 10^8 m/s and the frequency is 500,000 GHz (500,000 × 10^9 Hz), we can substitute these values into the formula:
wavelength = (3 × 10^8 m/s) / (500,000 × 10^9 Hz)
Simplifying the expression:
wavelength = (3 × 10^8) / (500,000) × (1 / 10^9) m
wavelength = (3 × 10^-1) × (1 / 10^-9) m
wavelength = 3 × 10^8 × 10^9 × 10^-9 m
wavelength = 3 × 10^8 × 10^0 m
wavelength = 3 × 10^8 m
To convert this wavelength to micrometers (μm), we need to multiply it by 10^6:
wavelength = 3 × 10^8 m × 10^6 μm/m
wavelength = 3 × 10^14 μm
Therefore, the wavelength of the given electromagnetic wave with a frequency of 500,000 GHz is 3 × 10^14 micrometers (μm).