The red supergiant Betelgeuse has a surface temperature of 3600 K.

a) Using the fact that the Sun's surface temperature is about 5800 K and that its continuous spectrum peaks at a wavelength of 500 nm, find the peak wavelength of Betelgeuse's continuous spectrum. (Please enter your answer in units of nanometers)

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/wien3.html

Thank you!

Ah, Betelgeuse, the cool cat of the supergiants! Well, since the Sun's surface temperature is around 5800 K with a peak wavelength of 500 nm, we can approximate the peak wavelength of Betelgeuse's continuous spectrum using its surface temperature of 3600 K.

Now, when it comes to temperatures, the peak wavelength is inversely proportional to the temperature. So, we can use a little math and a lot of humor to find the peak wavelength of Betelgeuse's continuous spectrum.

If the Sun's surface temperature is a hot tamale at 5800 K, and Betelgeuse's surface temperature is a slightly cooler jalapeño at 3600 K, then we can say that Betelgeuse's peak wavelength will be shifted towards the redder side of the spectrum.

Therefore, I'll put on my clown wig and tell you that the peak wavelength of Betelgeuse's continuous spectrum is around 800 nm. So, grab your red-tinted glasses, because Betelgeuse is painting the sky with its warm and toasty glow! 🌟✨

To find the peak wavelength of Betelgeuse's continuous spectrum, we can use Wien's displacement law.

Wien's displacement law states that the peak wavelength of an object's continuous spectrum is inversely proportional to its temperature.

We can set up the following equation using Wien's displacement law:

λ1 / λ2 = T2 / T1

Where:
λ1 is the peak wavelength of the Sun's continuous spectrum (500 nm)
T1 is the temperature of the Sun's surface (5800 K)
λ2 is the peak wavelength of Betelgeuse's continuous spectrum (to be calculated)
T2 is the temperature of Betelgeuse's surface (3600 K)

Let's solve for λ2:

λ2 = (λ1 * T2) / T1

λ2 = (500 nm * 3600 K) / 5800 K

λ2 = 310,800 nm K / 5800 K

λ2 ≈ 53.62 nm

Therefore, the peak wavelength of Betelgeuse's continuous spectrum is approximately 53.62 nanometers.

To find the peak wavelength of Betelgeuse's continuous spectrum, we can use Wien's Displacement Law, which states that the wavelength at which the peak of the blackbody radiation occurs is inversely proportional to the temperature of the object.

According to the question, the Sun's surface temperature is 5800 K, and its continuous spectrum peaks at a wavelength of 500 nm.

We can use this information to set up a proportion:

Sun's temperature / Sun's peak wavelength = Betelgeuse's temperature / Betelgeuse's peak wavelength

Writing this proportion:

5800 K / 500 nm = 3600 K / x

To solve for x, the peak wavelength of Betelgeuse's continuous spectrum, we can cross-multiply and then divide:

(5800 K) x = (3600 K) (500 nm)

Simplifying:

x = (3600 K) (500 nm) / 5800 K

Calculating:

x ≈ 310.35 nm

So, the peak wavelength of Betelgeuse's continuous spectrum is approximately 310.35 nm.