Suppose the sun expands so that its radius becomes `100` times its present radius and its surface temperature becomes half of its present value. The total energy emited by it then will increase by a factor of :

Options

A. `10^4`
B. 625
C. 256
D. 16

Answer

B

Explanation

Since, `Q prop r^2T^4`
`(Q_2)/(Q_1)=((r_2)/(r_1))_1^2 xx ((T_2)/(T_1))^4=(100)^2 xx (1/2)^4=625`