This question is about analysing the electromagnetic radiation from the star Beta Pictoris in the southern constellation of Pictor.
The peak wavelength of electromagnetic radiation from Beta Pictoris is 350 nm350\text{ nm}350 nm. The surface temperature of the Sun is 5800 K5800\text{ K}5800 K and the wavelength at which its maximum intensity is emitted is 500 nm500\text{ nm}500 nm.
The luminosity of Beta Pictoris is 3.2×1027 W3.2 \times 10^{27}\text{ W}3.2×1027 W.
Show that the surface temperature of Beta Pictoris is approximately 8300 K8300\text{ K}8300 K.
Estimate the radius of Beta Pictoris.
Electromagnetic radiation is collected from Beta Pictoris by a sensor on Earth with an efficiency of 12%12\%12% and cross-sectional area 4.0×10−4 m24.0 \times 10^{-4}\text{ m}^24.0×10−4 m2. The radiant power detected by the sensor is 3.6×10−15 W3.6 \times 10^{-15}\text{ W}3.6×10−15 W.
Calculate the intensity (radiant power per unit area) of the radiation arriving at the sensor from Beta Pictoris.
Calculate the distance of Beta Pictoris from Earth in light years.
