The total radiant energy per unit area, normal to the direction of incidence, received at a distance `R` from the centre of a star of radius `r` whose outer surface radiates as a black body at a temperature `T K` is given by
(where `sigma` is Stefan's constant)

Options

A. `sigmar^(2)T^(4)//R^(2)`
B. `sigma r^(2)T^(4)//4pir^(2)`
C. `sigmar^(4)T^(4)//r^(4)`
D. `4pisigmar^(2)T^(4)//R^(2)`

Answer

A

Explanation

In reaching a distance `R` this energy will be spread over a sphere of radius `R` , so the intensity of radiation will be given by
`S = (P)/(4 pi R^(2)) = (4 pi r^(2)sigmaT^(4))/(4 pi R^(2))`.