Question

Planetary Atmospheres. (a) The temperature near the top of Jupiter’s multicolored cloud layer is about . The temperature at the top of the earth’s troposphere, at an altitude of about , is about . Calculate the rms speed of hydrogen molecules in both these environments. Give your answers in m/s and as a fraction of the escape speed from the respective planet

(see Problem 18.72). (b) Hydrogen gas is a rare element in the earth’s atmosphere. In the atmosphere of Jupiter, by contrast, of all molecules are . Explain why, using your results from part (a). (c) Suppose an astronomer claims to have discovered an oxygen atmosphere on the asteroid Ceres. How likely is this? Ceres has a mass equal to the mass of the moon, a

density of , and a surface temperature of about

Short answer

(a) relation between RMS velocity and escape velocity for jupiter is

And the relation between Rms velocity and escape velocity for earth is

(b)As the escape velocity for jupiter is high so most of the hydrogen atom remain on jupiter surface

(c) it is difficult to find oxygen molecules in the asteroid's atmosphere.

Step-by-step solution

Step 1:About rms velocity and escape velocity

The root-mean square (RMS) velocity isthe value of the square root of the sum of the squares of the stacking velocity values divided by the number of values.

The minimum velocity with which a body should be thrown vertically upwards from the surface of the Earth so that it escapes the Earth's gravitational field is called the escape velocity (ve) of the body

Determine The RMS speed Of the Hydrogen Molecule for the earth and Jupiter

For Jupiter ,

Calculate For Earth ,

Therefore , relation between RMS velocity and escape velocity for Jupiter is

And the relation between Rms velocity and escape velocity for earth is

Determine the reason of presence of hydrogen atom on Jupiter surface

From the result in part A , the escape velocity on the earth is less than on the Jupiter so most molecule on the earth can reach the escape velocity while on Jupiter most hydrogen atom remain on due to high escape velocity

Therefore , As the escape velocity for Jupiter is high so most of the hydrogen atom remain on Jupiter surface

Determine the oxygen molecule on the asteroid surface

For calculation RMS and escape velocity for asteroid surface

To Calculate escape velocity find radius

From the result of rms and escape velocity we can obtain it will be difficult to find the oxygen molecule in asteroid atmosphere due to all the molecule will reach the escape velocity ad out of astroid

Therefore it is difficult to find oxygen molecules in the asteroid's atmosphere.