Final answer:
The frequency of the Earth's most intense infrared radiation with a wavelength of about 10.0 micrometers (assumed) is approximately 30 terahertz (THz), calculated using the speed of light and the formula for frequency.
Step-by-step explanation:
The question asks to find the frequency of electromagnetic radiation with a given wavelength of 10.0, which is assumed to be 10.0 micrometers (µm) since the Earth's most intense infrared radiation is around that wavelength. We can use the formula c = λf, where c is the speed of light (approximately 3 × 108 m/s), λ is the wavelength, and f is the frequency. To solve for frequency (f), we rearrange the equation to f = c / λ.
First, we convert the wavelength from micrometers to meters by multiplying 10.0 µm by 10-6 (since 1 µm = 10-6 m), giving us a wavelength of 10 × 10-6 meters. Then, we divide the speed of light by the wavelength: f = (3 × 108 m/s) / (10 × 10-6 m) = 3 × 1013 Hz. Thus, the frequency of the Earth's most intense infrared radiation is approximately 30 terahertz (THz).