A spherical star may be treated as an ideal blackbody

PHYSICS · Subjective · A Level · Physics · Astrophysics · Astrophysics

Problem

A spherical star may be treated as an ideal blackbody. (i) If the wavelength at which its emission spectrum peaks is

\lambda_{\max}

, express its absolute temperature

T

in terms of

\lambda_{\max}

. (Take the required constant as

b=2.898\times10^{-3}\,\text{m\,K}

.) (ii) Hence obtain an expression for the total power

P

radiated by the star in terms of its radius

R

and

\lambda_{\max}

alone. (The Stefan–Boltzmann constant is

\sigma=5.67\times10^{-8}\,\text{W\,m}^{-2}\text{K}^{-4}

.) (iii) The luminosity of the Sun is about

3.9\times10^{26}\,\text{W}

and its spectrum peaks near

500\,\text{nm}

. Using your result from part (ii), calculate the solar radius in metres, correct to two significant figures.