The radiation emitted by a star A is 10,000 times that of the sun. If the surface temperatures of the sun and the 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

`E_(A) = 10,000 E_(s)`
Radiation emitted, `E alpha AT^(4)`
`E_(A)/E_(s)=(r^(2)A)/(r^(2)s)(T_(A)/T_(s))^(4)`
`(10,000E_(s))/E_(s)=((rA)/(rs))^(2)((2000)/(6000))^(4)`
`10,000 = ((rA)/(rs))^(2)((1)/(81))`
`(rA)/(rs)=900`
`therefore` Radii of star A : radii of sun `= 900 : 1`