Question

1. The aurorae that occur on Saturn emit light in the ultraviolet (UV) and infrared (IR). Assuming the light is emitted at the low ends of the UV and IR spectrum, calculate the photon energies and temperatures of the auroras. On one of the initial flybys over the pole, your EM wave detector (a 1.00 m x 1.00 m panel made of a super thin sheet of gold) collected a 1.0 second snapshot the flux coming from those auroras. Calculate the fluxes of IR and UV radiation that the detector should read.

Answer 1

Energy of a photon is related to its wavelength by:

UV radiation has wavelength ranging from 100nm to 400nm.

So, UV radiation has photon energies 12.424eV to 3.106eV.

Infrared radiation has wavelength ranging from 750nm to 25000nm.

So, Infrared radiation has energies 1.656eV to 0.0497eV.

Use Wein's law for determining the temperature:

So, for UV radiation, the temperature range is: 7245K - 28980K.

Similarly, for Infrared radiation, the temperature range is:

115.92K - 3864K.

Area = 1m²

Using Stefan Boltzmann's law, the Flux will be:

Use this to determine the Flux for both UV and Infrared radiation.