At which temperature would the earth be radiating energy at the greatest rate or intensity?

The correct answer is E. 105o F.

The rate of radiation of energy from a body is proportional to the fourth power of its absolute temperature. This means that if the temperature of a body is doubled, the rate of radiation of energy will increase by a factor of 16.

At -5o F, the temperature of the Earth is about 263 K. At 105o F, the temperature of the Earth is about 388 K. This means that the rate of radiation of energy from the Earth at 105o F is about 256 times greater than the rate of radiation of energy from the Earth at -5o F.

The other options are incorrect because they are all lower temperatures than 105o F. At lower temperatures, the rate of radiation of energy is lower.