The sun radiates electromagnetic energy at the rate of 3.9 ×10^26 W. Its radius is 696 ×10^8 m

step 1 We are given that the energy rate which is nothing but the power generated by Sun that is equal

The sun radiates electromagnetic energy at the rate of 3.9...

The sun radiates electromagnetic energy at the rate of $3.9 \times 10^{26} \mathrm{~W}$. Its radius is $696 \times 10^{8} \mathrm{~m}$. The intensity of sunlight (in $\mathrm{Wm}^{-2}$ ) at the solar surface will be (a) $4.3 \times 10^{6}$ (b) $4.5 \times 10^{7}$ (c) $5.6 \times 10^{7}$ (d) $5.8 \times 10^{6}$

The sun radiates electromagnetic energy at the rate of $3.9 \times 10^{26} \mathrm{~W}$. Its radius is $696 \times 10^{8} \mathrm{~m}$. The intensity of sunlight (in $\mathrm{Wm}^{-2}$ ) at the solar surface will be
(a) $4.3 \times 10^{6}$
(b) $4.5 \times 10^{7}$
(c) $5.6 \times 10^{7}$
(d) $5.8 \times 10^{6}$

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Key Concepts

Surface Area of a Sphere

The surface area of a sphere is determined by the formula 4?r², where r is the radius of the sphere. This concept is essential when calculating how energy from a spherical radiator, such as a star, is distributed over space, thereby affecting the intensity at various distances.

Inverse Square Law

The inverse square law states that the intensity of radiation from a point source diminishes proportionally to the square of the distance from the source. It is critical in astrophysics for understanding how the energy emitted from an object spreads out, influencing the measured intensity at different distances.

Luminosity

Luminosity is the total power output of an object, such as a star, and represents the total amount of energy it emits per unit time. In astrophysics, it is a key parameter for characterizing stars and other celestial bodies, as it determines the overall energy available to be distributed across space.

Intensity of Radiation

Intensity refers to the power per unit area received from a radiating source. It is calculated by dividing the luminosity by the area over which the energy is distributed, which for spherical objects is the surface area of a sphere. This provides insight into how much energy is delivered at a particular location.

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