b
For the condition of thermal equilibrium the energy received by earth should be equal to the energy transmitted by earth.

\(\frac{T_{ s }^{4} 4 \pi R_{ s }^{2}}{4 \pi d^{2}} \times \pi R_{e}^{2}=\sigma \rho T_{e}^{4} 4 \pi R_{e}^{2}\)

\(T_{c}^{4}=\frac{T_{ s }^{4} R_{ s }^{2}}{4 e d^{2}}\) \(....(I)\)

Substitute \(6000\) for \(T_{s}, 7 \times 10^{8}\) for \(R_{5}, 2 \times 10^{11}\) for \(d\) and \(0.6\) for \(e\) in equation \((I).\)

\(T_{ e }^{4}=\frac{(6000)^{4}\left(7 \times 10^{8}\right)^{2}}{4\left(2 \times 10^{11}\right)^{2} \times 0.6}\)

\(=\frac{36 \times 36 \times 7 \times 7}{4 \times 4 \times 0.6} \times 10^{6}\)

\(=66.15 \times 108\)

\(T_{ e } \approx 300 K\)