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CHAPTER 45 - 8

# CHAPTER 45 - 8 - , LAT =4pr T Whenweformtheratio,weget 2 4...

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From the Stefan-Boltzmann law, the absolute luminosity depends on the radius of the star and the temperature: L     AT 4  = 4p r 2 T 4 . When we form the ratio, we get L 2 / L 1  = ( r 2 / r 1 ) 2 ( T 2 / T 1 ) 4  = ( r 2 / r 1 ) 2 ( λ 1 / λ 2 ) 4 ; (2 × 10 27  W)/(10 26  W) = ( r 2 / r 1 ) 2 (600 nm/400 nm) 4 , which gives  r 2 / r 1  =      2 . 43. We find half the subtended angle from φ  = 1/30 pc = (1/30) /(3600 / ° ) ˜ (1 × 10 –5 ) ° . Thus the minimum subtended angle is       ˜ (2 × 10 –5 ) ° . 44. The wavelengths for the same transition in hydrogen-like atoms are given by 1/ λ  = (constant) Z 2 . Thus we have λ / λ  =  λ H / λ He  = ( Z He / Z H ) 2  = (2/1) 2  =  { [1 + ( v / c )]/[1 – ( v / c )] } 1/2 , which gives  v  =       0.88 c . 45. We find the temperature from E  =  * kT ,   or    T  =  % Mc 2 / k  =  % (1.8 TeV)(1.60 × 10 –7  J/TeV)/(1.38 × 10 –23  J/K) =      1.4 × 10 16  K .

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CHAPTER 45 - 8 - , LAT =4pr T Whenweformtheratio,weget 2 4...

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