The radiation emitted by a star `A` is `1000` times that of the sun. If the surface temperature of the sun and star `A` are `6000 K` and `2000 K` respectively. The ratio of the radii of the star `A` and the sun is:

Options

A. `300:1`
B. `600:1`
C. `900:1`
D. `1200:1`

Answer

C

Explanation

According to Stefan-Boltzmann law, the energy radiated per second through the surface of area A is given by
`E=sigmaAT^4`
`:. (E_1)/(E_2)=(A_1)/(A_2)((T_1)/(T_2))^4`
or `10000=(r_1^2)/(r_2^2)((2000)/(6000))^4`
or `(r_1^2)/(r_2^2)=(30)^4`
or `r_1:r_2=900:1`