Earths temperature averaged over the year is about 300 Kelvin. At what wavelength does it radiate most strongly? What part of the electromagnetic spectrum does this wavelength lie in? Can you see it?
http://csep10.phys.utk.edu/astr162/lect/light/planck.html
Well, let me put on my clown nose and give you a funny answer! Earth's temperature may be hot, but it's not as scorching as my failed stand-up career. Now, when it comes to the wavelength at which Earth radiates most strongly, it falls in the infrared part of the electromagnetic spectrum. But here's the punchline: you can't see it with your naked eye! It's like a great comedian performing in the dark – you can feel the heat, but you can't see the jokes.
To determine the wavelength at which Earth radiates most strongly, we can use Planck's law of blackbody radiation. According to Planck's law, the peak wavelength (λ_max) is dependent on the temperature of the object.
1. Convert the average temperature of Earth from Celsius to Kelvin:
Earth's temperature ≈ 27 degrees Celsius = 300 Kelvin
2. Planck's law states:
λ_max = 2.898 × 10^-3 Kelvin·meters / Earth's temperature
3. Calculate the peak wavelength:
λ_max = 2.898 × 10^-3 / 300 ≈ 9.66 × 10^-6 meters ≈ 9.66 micrometers
The wavelength at which Earth radiates most strongly is approximately 9.66 micrometers.
Now, let's determine which part of the electromagnetic spectrum this wavelength lies in and whether it is visible to the human eye:
The electromagnetic spectrum spans a wide range of wavelengths, from radio waves to gamma rays. The visible spectrum, which can be detected by the human eye, ranges from approximately 400 to 700 nanometers.
Converting 9.66 micrometers to nanometers:
1 micrometer = 1,000,000 nanometers
9.66 micrometers ≈ 9,660 nanometers
As 9,660 nanometers (or 9.66 micrometers) is outside the range of the visible spectrum, it falls within the infrared part of the electromagnetic spectrum. The human eye cannot see infrared radiation.
Therefore, the wavelength at which Earth radiates most strongly is in the infrared part of the electromagnetic spectrum and is not visible to the human eye.
To determine at which wavelength Earth radiates most strongly, we can use a concept known as Wien's displacement law, which states that the peak wavelength of blackbody radiation is inversely proportional to its temperature.
First, convert Earth's average temperature of 300 Kelvin to Celsius by subtracting 273.15. This gives us 26.85 degrees Celsius.
Next, we can use the formula provided in the link you shared, which is:
Wavelength = (2.9 * 10^(-3)) / Temperature
Plugging in the value of Earth's temperature, we get:
Wavelength = (2.9 * 10^(-3)) / 300 ≈ 9.67 * 10^(-6) meters
This wavelength lies in the infrared part of the electromagnetic spectrum. Infrared radiation has longer wavelengths than visible light, so it is not visible to the naked eye. However, it can be detected by specialized instruments such as infrared cameras.
Therefore, Earth radiates most strongly at a wavelength of approximately 9.67 * 10^(-6) meters in the infrared part of the electromagnetic spectrum, which is not visible to humans.