Wien’s radiation law says that the wavelength of most intense radiation (λmax) emitted by a blackbody is inversely proportional to the absolute temperature (T) of the object. The surface of the Sun radiates as a blackbodyat a temperature ofT=6000 kelvins so that the Sun’sλmaxis 0.48 micrometers.The Earth system radiates as a blackbody at a temperature of T = 255 kelvins so that the Earth’s λmaxis 11.4 micrometers.
a. The Sun’s radiationis most intense in the [(ultraviolet) (visible) (infrared)(microwave)] portion of the electromagnetic spectrum.
b. The Earth’s radiation is most intense in the [(ultraviolet) (visible) (infrared) (microwave)] portion of the electromagnetic spectrum.
a. (ultraviolet)
b. (microwave)
This question is so important to us that I am going to answer it just to make sure you know.
Radiation comes in from the sun in a wide spectrum but maximum ultraviolet although as you know there is lots of visible. That energy mostly gets used to power things like plants and animals and soil on earth and warm things up.
Those warm things radiate back out toward space maximum in the infrared (heat) wavelengths.
The balance between that incoming short wavelength power and the outgoing infrared power to a great extent determines the temperature of earth's surface. If something (like CO2 or Methane) in the atmosphere hinders the radiation of that infrared out toward space, the earth surface gets warmer.
To determine the answers to these questions, we need to understand that Wien's radiation law states that the wavelength of most intense radiation emitted by a blackbody is inversely proportional to the absolute temperature of the object.
a. We are given that the Sun's temperature is 6000 kelvins, and its λmax is 0.48 micrometers. Using Wien's radiation law, we can conclude that the Sun's radiation is most intense in the infrared portion of the electromagnetic spectrum. As the temperature of an object increases, the λmax decreases, and the peak of the radiation shifts towards shorter wavelengths. In this case, the Sun's temperature is relatively high, resulting in a shorter λmax, which falls in the infrared range.
b. For the Earth, we know that its temperature is 255 kelvins, and its λmax is 11.4 micrometers. Applying Wien's radiation law, we can infer that the Earth's radiation is most intense in the infrared portion of the electromagnetic spectrum as well. As the temperature decreases, the λmax increases, and the peak of the radiation shifts towards longer wavelengths. With the Earth having a lower temperature compared to the Sun, its λmax is longer, falling in the infrared range.
Therefore, the answers are:
a. The Sun's radiation is most intense in the infrared portion of the electromagnetic spectrum.
b. The Earth's radiation is most intense in the infrared portion of the electromagnetic spectrum.