Question

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

• A. $1600:1$
• B. $1800:1$
• C. $16:1$
• D. $25:1$

Answer 1

Answer: (A)

As $E=Q=A{T}^4\Rightarrow Q=\pi r^2{T}^4$
$\therefore \frac{Q_{star}}{Q_{sun}}=\frac{r_{star}^2.T_{star}^4}{r_{sun}^2.T_{sun}^4}=\frac{10000}{1}$
$={\left(\frac{r_{star}}{r_{sun}}\right)}^2{\left(\frac{2000}{8000}\right)}^4$
$10000\times 256={\left(\frac{r_{star}}{r_{sun}}\right)}^2$
$\frac{r_{star}}{r_{sun}}=\frac{1600}{1}$