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

Answer

B

Explanation

As energy radiated per unit time , `E=sigmaepsilonAT^(4)`
According to question ,`E"star"=10000E_("sun")`
`rArr" "E"star"xxT"star"^(4)=10000A_("sun")xxT_("sun")^(4)`
`piR_("star")^(2)T_("star")^(4)=10000xxpiR_("sun")^(2)xxT_("sun")^(4)`
`(R_("star")/(R_("sun")^(2)))^(2)=1000((6000)/(2000))^(4)`
`R_("star")/(R_("sun"))=sqrt(10000xx3^(4))=(900)/(1)`