Download Wien`s Law

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.
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
T ( K) 
2.9  10 K  nm
6
Max in nm
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
Visible
400 nm to 700 nm
Infrared (IR)
Above 700 nm
The relationship between the maximum intensity of a star and its temperature is
T ( K) 
2.9  10 6 K  nm
Max in nm
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?
Solution:
T (K) 
2.9  10 6 K  nm
Max in nm
2.9  10 6 K  nm

 5,272 K
550 nm
Answer in a sentence: The star has a temperature of 5,272 K.
The relationship between the maximum intensity of a star and its temperature is
T ( K) 
2.9  10 6 K  nm
Max in nm
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?
Solution:
T (K) 
2.9  10 6 K  nm
Max in nm
2.9  10 6 K  nm

 20,000 K
145 nm
Answer in a sentence: The star has a temperature of 20,000 K.
The relationship between the maximum intensity of a star and its temperature is
T ( K) 
2.9  10 6 K  nm
Max in nm
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?
Solution:
Answer in a sentence: The star has a temperature of 2,417 K.
The relationship between the maximum intensity of a star and its temperature is
T ( K) 
2.9  10 6 K  nm
Max in nm
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?
Solution:
Answer in a sentence: The star has a temperature of 2,417 K.
The relationship between the maximum intensity of a star and its temperature is
T ( K) 
2.9  10 6 K  nm
Max in nm
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?
Solution:
2.9  10 6 K  nm
T ( K) 
Max in nm
 Max in nm
2.9  10 6 K  nm 2.9  10 6 K  nm


 290 nm
T ( K)
10,000 K
Answer in a sentence: The star radiates most intensely at 290 nm which is in the
ultraviolet portion of the electromagnetic spectrum.
The relationship between the maximum intensity of a star and its temperature is
T ( K) 
2.9  10 6 K  nm
Max in nm
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?
Solution:
Answer in a sentence: The star radiates most intensely at 1,160 nm which is in the
infrared portion of the electromagnetic spectrum.
The relationship between the maximum intensity of a star and its temperature is
T ( K) 
2.9  10 6 K  nm
Max in nm
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?
Solution:
Answer in a sentence: The star radiates most intensely at 414 nm which is in the
visible portion of the electromagnetic spectrum.
The relationship between the maximum intensity of a star and its temperature is
T ( K) 
2.9  10 6 K  nm
Max in nm
Practice Problem 8: Why would life be difficult around a typical O-star?
Solution: Hint – use the typical temperature of an O-star to determine the portion of
the electromagnetic spectrum in which it radiates most intensely.
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.
The relationship between the maximum intensity of a star and its temperature is
T ( K) 
2.9  10 6 K  nm
Max in nm
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?
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.
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).