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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 proportional to:

1. r²σ(T + 273)^4 / 4πR²
2. 16π²r²σT⁴ / R²
3. 1/R²
4. r²σT⁴ / R²

Correct answer: r²σT⁴ / R²

Solution

The power radiated by the Sun as a black body is proportional to its surface area and temperature raised to the fourth power (Stefan-Boltzmann law). At a distance R, the power received per unit area is inversely proportional to R² due to the spherical spreading of radiation. Hence, the correct formula is r²σT⁴ / R².

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