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In solar radiation, the intensity of radiation is maximum around the wavelength $λ$ . If R is the radius of the sun and c is the velocity of light, the mass lost by the sun per second is proportional to:

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$\frac{R^{2}}{λ^{4} c^{2}}$

$\frac{R^{2}}{λ^{2} c^{2}}$

$\frac{R^{3}}{λ^{4} c^{3}}$

$\frac{R^{3}}{λ^{4} c^{2}}$

answer is A.

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Detailed Solution

According Stefan’s law
$\frac{Q}{t} = σ 4 {πR}^{2} T^{4} = {mc}^{2}$
Where m is the mas converted to energy per sec. but $λ_{m} T = constant$
$T \propto \frac{1}{λ}$
$m = \frac{σ 4 {πR}^{2} T^{4}}{c^{2}} \propto \frac{R^{2}}{λ^{4} c^{2}}$

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