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 8000 K and 2000 K respectively. The ratio of the radii of the star A and the sun is

Options

A. `1600: 1 `
B. `1800 : 1 `
C. `16: 1`
D. `25 :1 `

Answer

A

Explanation

As `E = Q = AT^(4) implies Q = pi r^(2) T^(4)`
`:. (Q_("star"))/(Q_("sun")) = (r_("star")^(2) . T_("star")^(4))/(r_("sun")^(2) . T_("sun")^(4))= (1000)/(1)`
`=((tau_("star"))/(tau_("sun")))^(2) ((2000)/(8000))^(4)`
`10000 xx 256 = ((r_("star"))/(r_("sun")))^(2)`
`(r_("star"))/(r_("sun")) = (1600)/(1)`
Hence, the required ratio is 1600 : 1