Question

The radiation emitted by a star A is 10,000 times that of the sun. If the surface temperature of the sun and the star A are 6000K and 2000K respectively, then 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

The correct option is C 900 : 1

We know that: $E=\sigma ϵA{T}^4$ and it is given that $E_{star}=10000\times E_{sun}$
$T_{star}=2000K$, $r_{star}=r_1$
$T_{sun}=6000K$, $r_{sun}=r_2$

$\frac{E_{star}}{E_{sun}}=\frac{r_1^2\times T_1^4}{r_2^2\times T_2^4}$

$\frac{{10000\times E}_{sun}}{E_{sun}}=\frac{r_1^2\times (2000{)}^4}{r_2^2\times ({6000)}^4}$

$\Rightarrow \frac{r_1}{r_2}=900$