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

Answer

A

Explanation

If r is the radius of the star and T its temperature , then the energy emitted by the star per second through radiation in accordance with Stefan's law will be given by
`AsigmaT^(4)=4pir^(2)sigmaT^(4)`
In reaching a distance R this energy will spread over a sphereof radius R ,so the intensity of radiation will be given by
`S=(P)/(4piR^(2))=(4pi^(2)sigmaT^(4))/(4piR^(2))=(sigmar^(2)T^(4))/(R^(2))`