Horizons: Exploring the Universe (MindTap Course List)
Horizons: Exploring the Universe (MindTap Course List)
14th Edition
ISBN: 9781305960961
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 9, Problem 12P
To determine

How luminous will it be if a contracting protostar is five times the radius of the Sun and hasa temperature of only 2000 K?

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Suppose a protostar has a luminosity of 157,341 Lo and a surface temperature of 4,540 K (Kelvins). What is the radius of this protostar? [Enter your answer as a multiple of the Sun's radius. I.e., if you find R = 20 Ro enter 20. This problem is easier if you start with the relevant equation and create a ratio using the Sun's values. Recall that the Sun has a surface temperature of 5778 K. ]
If a contracting protostar is seven times the radius of the Sun and has a temperature of only 2030 K, how luminous will it be relative to the Sun? (Hint: Use the luminosity-radius-temperature relation: (L/L) = (R/R.)^2 (T/T.)^4 The surface temperature of the Sun is 5800 K.) (L/L.) = ?
If the hottest star in the Carina Nebula has a surface temperature of 51,000 K, at what wavelength (in nm) does it radiate the most energy?  Hint: Use Wien's law:  ?max =  2.90 ✕ 106 nm · K T How does that compare with 91.2 nm, the wavelength of photons with just enough energy to ionize hydrogen? -The wavelength calculated above is shorter than 91.2 nm. Photons at this calculated wavelength will have more than enough energy to ionize hydrogen. -The wavelength calculated above is longer than 91.2 nm. Photons at this calculated wavelength will have more than enough energy to ionize hydrogen.   -The wavelength calculated above is shorter than 91.2 nm. Photons at this calculated wavelength will not have enough energy to ionize hydrogen. -The wavelength calculated above is longer than 91.2 nm. Photons at this calculated wavelength will not have enough energy to ionize hydrogen.
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