Find the radius rrigel of the star rigel, the bright blue star in the constellation orion that radiates energy at a rate of 2.7×1031w and has a surface temperature of 11,000 k. assume that the star is spherical. use σ=5.67×10−8w/m2⋅k4 for the stefan-boltzmann constant and express your answer numerically in meters to two significant figures.

Explanation:

The Stefan–Boltzmann law for a black body (as stars are treated) can be written as , where is the total energy radiated per unit surface area across all wavelengths per unit time, the absolute temperature and is the Stefan–Boltzmann constant.

If we multiply by the surface area of the star we get the total energy radiated across all wavelengths per unit time, which is the total power radiated, so we can write:

where we have used the formula for the surface area of a sphere

Solving for r we have:

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.