The intensity of sunlight falling on the earth is about 1.4 kw/m2 (before any gets absorbed by our atmosphere). at what rate does the sun emit light energy? (the earth-sun distance = 1.5 × 108 km and the earth's radius = 6.4 × 103 km.)

The area of the Earth (Ae) that is irradiated by is given by:

Ae = 4πRe^2, where Re = Distance from Sun to Earth
Substituting;
Ae = 4π*(1.5*10^8*1000)^2 = 2.827*10^23 m^2

On the Earth, insolation (We) = Psun/Ae

Therefore,
Psun (Rate at which sun emits energy) = We*Ae = 1.4*2.827*10^23 = 3.958*10^23 kW = 3.958*10^26 W

The answer is trial 3.