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. `(sigma r^(2) T^(4))/(R^(2))`
B. `(sigma r^(2)T^(4))/(4pi r^(2))`
C. `(sigma r^(4) T^(4))/(r^(4))`
D. `(4pi sigma r^(2) T^(4))/(R^(2))`

Answer

A

Explanation

According to the Stefan Boltzmann law, the power radiated by the star whose outer surface radiates as a black body at temperature TK is given by
`P rho = sigma 4pi r^(2) T^(4)`
where, r= radius of the star `sigma` Stefan.s constant
The radiant power per unit area received at a distance R from the centre of a star is `S= (P)/(4pi R^(2)) = (sigma 4pi r^(2)T^(4))/(4pi R^(2)) = (sigma r^(2)T^(4))/(R^(2))`