Question

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

Answer 1

Correct Answer - C
According to Stefan-Boltzmann law, the energy radiated per second through the surface of area `A` is given by
`E = sigma AT^(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`.