1. Review of the Wien’s Law Review Chapter 11.1.4 Color and Temperature in AstronomyNotes for a more complete discussion of the details of this relationship.

2. Wien’s Law relates the wavelength of maximum intensity of a star to its temperature The relationship between the maximum intensity of a star and its temperature is where the temperature T is in Kelvins and the wavelength of maximum intensity is in nanometers Portion of the EM Spectrum Wavelength range, nm Ultraviolet (UV)Below 400 nm Visible400 nm to 700 nm Infrared (IR)Above 700 nm

3. The relationship between the maximum intensity of a star and its temperature is Practice Problem 1: A star has its maximum intensity in the visible portion of the electromagnetic spectrum at a wavelength of 550 nm. What is its temperature? Answer in a sentence: The star has a temperature of 5,272 K. Solution:

4. The relationship between the maximum intensity of a star and its temperature is Practice Problem 2: A star has its maximum intensity in the ultraviolet portion of the electromagnetic spectrum at a wavelength of 145 nm. What is its temperature? Answer in a sentence: The star has a temperature of 20,000 K. Solution:

5. The relationship between the maximum intensity of a star and its temperature is Practice Problem 3: A star has its maximum intensity in the infrared portion of the electromagnetic spectrum at a wavelength of 1,200 nm. What is its temperature? Answer in a sentence: The star has a temperature of 2,417 K. Solution:

6. The relationship between the maximum intensity of a star and its temperature is Practice Problem 4: A star has its maximum intensity in the infrared portion of the electromagnetic spectrum at a wavelength of 1,200 nm. What is its temperature? Answer in a sentence: The star has a temperature of 2,417 K. Solution:

7. The relationship between the maximum intensity of a star and its temperature is Practice Problem 5: If a star has a temperature of 10,000 K in what portion of the electromagnetic spectrum does it radiate with maximum intensity? Answer in a sentence: The star radiates most intensely at 290 nm which is in the ultraviolet portion of the electromagnetic spectrum. Solution:

8. The relationship between the maximum intensity of a star and its temperature is Practice Problem 6: If a star has a temperature of 2,500 K in what portion of the electromagnetic spectrum does it radiate with maximum intensity? Answer in a sentence: The star radiates most intensely at 1,160 nm which is in the infrared portion of the electromagnetic spectrum. Solution:

9. The relationship between the maximum intensity of a star and its temperature is Practice Problem 7: If a star has a temperature of 7,000 K in what portion of the electromagnetic spectrum does it radiate with maximum intensity? Answer in a sentence: The star radiates most intensely at 414 nm which is in the visible portion of the electromagnetic spectrum. Solution:

10. The relationship between the maximum intensity of a star and its temperature is Practice Problem 8: Why would life be difficult around a typical O-star? Answer in a sentence: A typical O-star at 50,000 Kelvins will emit most intensely at 58 nm far into the UV portion of the electromagnetic spectrum. These hard UV photons from the star would be very dangerous to life exposed to them. Solution: Hint – use the typical temperature of an O-star to determine the portion of the electromagnetic spectrum in which it radiates most intensely.

11. The relationship between the maximum intensity of a star and its temperature is Practice Problem 8: Plants utilize photosynthesis to create the energy they need to survive, grow and reproduce. Photosynthesis is most sensitive to a red-light photons of wavelength near 6,700 nm to create energy for the plant. What main sequence spectral type star is best matched to drive photosynthesis most efficiently? Answer in a sentence: A star with temperature of 4,328 Kelvins will radiate most intensely at 670 nm. This temperature corresponds to a mid-K star (K3 through K6). Solution: Hint – determine the temperature of a star that radiates most intensely where photosynthesis is most sensitive and then look up or interpolate the spectral type that would have that wavelength at maximum intensity.