Problem
A. Maxwell-Boltzmann Distribution
I. Explain the Maxwell and Maxwell-Boltzmann distributions. Derive a) the mean speed and b) the most probable speed of a particle assuming in both cases the Maxwell-Boltzmann distribution of speed.
II. Calculate the mean free path of O and O2, at the standard temperature and pressure, STP. Assume the diameter of O2 is twice the diameter of O.
III. Plot the Maxwell-Boltzmann distribution with the help of your preferred programming language (eg. Fortran, Matlab, Python, Maple, etc.) for: CO2 at 300K and 2 other temperatures (160K and 2000K). Do the same at 300K for 3 different gases (N2, He, H).
i. Explain the shape of the plots. What are the reasons for the differences in the plots?
ii. Attach the code of your programme.
iii. Calculate the most probable speed for CO2 at 270 K according to the Maxwell-Boltzmann distribution.
IV. Why does the Earth have an atmosphere where as the Moon does not? Calculate the escape velocity for the Earth and the Moon. Compare these values with your previous results.
B. Magnetosphere and Ionosphere
I. Why does the Earth have a magnetic field? Give examples of planets or satellites which do not have magnetic fields. Explain the origin of ionosphere on the Earth.
II. What characterizes the ionospheric regions D, E and F. For example, what are the main constituents and the sources of ionization?
III. Make a sketch of the electron density in the ionosphere during the day and night. Explain the diurnal variations.
IV. Explain the difference in radio wave transmission between day and night.
V. To explore the ionosphere scientifically, an ionosonde is used. How does it work?