# Caclulate the root mean square

## Homework Statement

There is almost no helium gas in the earth’s atmosphere - indeed the price of He has increased in
recent times due to worries about a limited supply. (Bad news for parties and for all the scientists
who use liquid He as a coolant.) we know that the “escape velocity” required
to escape from the earth’s gravitational field is ⇠11.2km/s. Explain using physical concepts,
and kinetic theory in particular, why there is very little He gas in the atmosphere. Start by
calculating the root mean square (rms) speed of Helium (He) gas in the upper atmosphere,
assuming a temperature of 2000 K. Note that the atomic weight of He' 4, where 1 atomic mass
unit = 1.67 ⇥ 10−27kg

v=sqrt(3kt/m

## The Attempt at a Solution

I did the equation since we were given K is constant 1.38x10^-23 J/k i subbed the value inside and I got
v=sqrt(3(1.38x10^-23)(2000)/6.644x10^-27) Note I did find mass using mm and avogardos number. I got number of 3530.2m/s and escape velocity is in km/s that is if it converted to m/s it's way higher than the velocity calculated which doesn't make sense. I expected velocity to be higher... any help is appereciated :)

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DrClaude
Mentor
The number you calculated is correct. Remember that you are only calculating the rms velocity. What can you say about the velocity distribution?

• Bystander
It's lower than the veloicty escape? which is 11.2kms which is around 11.2k m/s?

Bystander
Homework Helper
Gold Member
distribution
Or, range.

Am i right then?

DrClaude
Mentor
Am i right then?
Well, you haven't answered the question. Why is there little helium in the atmosphere?