# Caclulate the root mean square

• Derek1997
In summary, the lack of helium gas in the earth's atmosphere is due to its low root mean square velocity, which is lower than the escape velocity required to leave the earth's gravitational field. This can be explained by kinetic theory and the atomic weight of helium.
Derek1997

## 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 :)

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?

DrClaude said:
distribution
Or, range.

Am i right then?

Derek1997 said:
Am i right then?
Well, you haven't answered the question. Why is there little helium in the atmosphere?

## 1. What is the formula for calculating the root mean square?

The formula for calculating the root mean square is √[(x1^2 + x2^2 + ... + xn^2)/n], where x1, x2, ... xn are the values being squared and n is the total number of values.

## 2. What is the purpose of calculating the root mean square?

The root mean square is used to find the average value of a set of numbers, taking into account the magnitude of each number. It is commonly used in statistics and physics to represent the overall magnitude of a set of values.

## 3. How is the root mean square different from the arithmetic mean?

The arithmetic mean is calculated by adding all the values in a set and dividing by the total number of values, while the root mean square involves squaring each value and taking the square root of the average of those squared values. This means that the root mean square gives more weight to larger values in the set.

## 4. Can the root mean square be negative?

No, the root mean square cannot be negative. Since it involves squaring all the values in a set, the result will always be positive or 0. If the result is 0, it means that all the values in the set are 0.

## 5. What is the significance of the root mean square in real-life applications?

The root mean square is commonly used in various fields, such as engineering, physics, and finance. It can be used to calculate the average power of a signal, estimate the average velocity of particles, and determine the volatility of financial assets.

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