Question

The radiation emitted by a star A is 10000 times that of the sun. If the surface temperatures 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

Answer: (C)

900 : 1

Answer 2

e µ AT⁴ ; e µ R² T⁴ or R µ $\sqrt{\frac{\varepsilon}{T^{4}}}$

$\frac{R_{2}}{R_{1}}$= $\sqrt{\frac{\varepsilon_{2}}{\varepsilon_{1}}.\frac{T_{1}^{4}}{T_{2}^{4}}}$ = $\sqrt{\frac{10000}{1} \times \left( \frac{6000}{2000} \right)^{4}}$

= 10² × $\left( \frac{3}{1} \right)^{2}$ = 900 : 1