Question

1. For an atmosphere in hydrostatic equilibrium the variation of particle number density (# of particles per unit volume) of each species as a function of altitude (z) is found by equating gravitational and pressure forces. The resulting expression is: N(z) = No * e^(-(z - zo)/H) where N0 is a constant for each species, and z0 is an arbitrary reference altitude. The parameter H is called the scale height, which is equal to KT/mg. In the scale height expression K is Boltzmann’s constant, T is the temperature, m is the species mass, and g is the local gravitational constant. At high thermospheric altitudes the UV and EUV radiation is intense enough to break down both O2 and H2 into their monatomic forms: O and H. Imagine that a high-altitude spacecraft measures a neutral H number density of 2x105 cm-3 at an altitude of 1000 km, and a lower altitude satellite simultaneously measures a neutral O density of 5x107 cm-3 at the same latitude and longitude, but at an altitude of 300 km.

a. If the temperature of the thermosphere is constant at 1600 Kelvin, calculate the altitude of the “transition height”, which is defined as the height at which the densities of H and O are equal. Like most atmospheric quantities, the transition height varies as a function of time, location, solar cycle, and season.

b. Repeat the calculation to find the transition height for a temperature of 1000 Kelvin.

c. Verify your answers by using the scale height equation to plot the O number density for altitudes between 100 and 1500 km, and the H number density from 500-1500 km (below 500 km there is very little H, because it is so light that it has a large thermal speed and rapidly diffuses upward). Use a linear scale for altitude on the y-axis, and plot the density variations on a linear scale on the x-axis. Show your results for both cases “a” and “b” on the same set of axes, indicating on the plot which

Answer 1

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