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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)
- σr²T⁴/R²
- σr²T⁴/4πR²
- R²σT⁴/r⁴
- 4πσr²T⁴/R²
Correct answer: σr²T⁴/4πR²
Solution
The total radiant energy per unit area is given by the Stefan-Boltzmann law. The power radiated by the star is proportional to its surface area (4πr²) and T⁴. At a distance R, this energy spreads over a sphere of surface area 4πR². Thus, the energy per unit area is σr²T⁴/4πR².
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