Assuming the sun to have a spherical outer surface of radius `r` radiating like a black body at temperature `t^(@)C`. The power received by a unit surface (normal to the incident rays) at a distance `R` from the centre of the sun is
where `sigma` is the Stefan's constant.

Options

A. `(4 pi r^(2) sigma t^(4))/(R^(2))`
B. `(r^(2) sigma (t + 273)^(4))/(4 pi R^(1))`
C. `(16 pi^(2) r^(2) sigma t^(4))/(R^(2))`
D. `(r^(2) sigma (t + 273)^(4))/(R^(2))`

Answer

D

Explanation

(4) `u = sigma A T^(4) = sigma. 4 pi r^(2) (t + 273)^(4)` Intensity reached at earth
`I = (sigma . 4 pi r^(2) (t + 273)^(4))/(4 pi R^(2))`
`= (r^(2) sigma (t + 273)^(4))/(R^(2))`