Question

An oxygen molecule is moving near the earth's surface. Another oxygen molecule is moving in the ionosphere (the uppermost part of the earth's atmosphere) where the Kelvin temperature is three times greater. Determine the ratio of the translational rms speed in the ionosphere to the translational rms near the earth's surface.'

Answer 1

Answer:

The ratio of the translational rms speed in the ionosphere to the translational rms near the earth's surface is $\sqrt 3 :1$

Explanation:

The relation between the translational rms speed and the temperature is given by :

$v_{rms}=\sqrt{\dfrac{3kT}{m}}$

So, $v_{rms}\propto \dfrac{1}{\sqrt{T} }$

When the temperature is three times greater.  

$v'_{rms}=\dfrac{1}{3T}$

The ratio of the translational rms speed in the ionosphere to the translational rms near the earth's surface is :

$\dfrac{v_{rms}}{v'{rms}}=\dfrac{\sqrt 3}{1}$

Hence, this is the required solution.