An Introduction to Modern Astrophysics · Problem 11.7

The Interstellar Medium and Star Formation — Carroll & Ostlie

Physics — Astrophysics · blackbody-radiation-ratio

Problem

(a) Using Eq. (3.22), show that in the Sun's photosphere, ln⁡(Ba/Bb)≈11.5+hckT(1λb−1λa)\ln (B_a/B_b) \approx 11.5 + \frac{hc}{kT}\left(\frac{1}{\lambda_b} - \frac{1}{\lambda_a}\right) where Ba/BbB_a/B_b is the ratio of the amount of blackbody radiation emitted at λa=10\lambda_a = 10 nm to the amount emitted at λb=100\lambda_b = 100 nm, centered in a wavelength band 0.1 nm wide. (b) What is the value of this expression for the case where the temperature is taken to be the effective temperature of the Sun? (c) Writing the ratio in the form Ba/Bb=10xB_a/B_b = 10^x, determine the value of xx.

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