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 σ is Stefan’s constant)

Options

(a) σr²T⁴ / R²
(b) σr²T⁴ / 4πr²
(c) σr⁴T⁴ / r⁴
(d) 4π σr²T⁴ / R²

Correct Answer:

σr²T⁴ / R²

Explanation:

E = S / S₀ σT⁴ = 4πr² / 4πR² σT⁴
σr²T⁴ / R²