The solar constant is defined as the average flux of solar energy incident on the outer fringes of the Earth's atmosphere and a commonly used value is \(1.353 \mathrm{~kW} / \mathrm{m}^{2}\). If the Sun has a diameter of \(1.39 \times 10^{6} \mathrm{~km}\) and is assumed to radiate like a black body, what is its effective temperature?

If the Sun is treated as a black body with a temperature of \(5765 \mathrm{~K}\), show that \(99 \%\) of the radiation emitted by the Sun is in the wavelength range 0.25-3.96 \(\mu \mathrm{m}\).