What is the movement of Helium molecule? Please provide a graphic display, drawing or photgraph.

That is your work. Our work here is to help, not do the work of others. As such, you should know about the Brownian motion, the randomness in the motion of molecules.

No Unrelevant an out of proportion answers please... I know about the Brownian Motion... the only thing is that I can't find an exact illustration of that motion which I will be using in my Architectural Design

You'll be using it in architecture? I'm curious of how... do you mind giving more details please?

The movement of a molecule depends a lot on its temperature. But how it vibrates is specific to the kind of molecule. Do you mean vibration? Molecules have three kinds of movement. Which do you mean? Not sure what the question is. Need more background.

Check out this, for example.

Molecular vibration - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Molecular_vibration)

My question is what is the movement of Helium Molecule... and I am associating the idea of change in the speed at which the molecules of noble gases if applied external force like heat... I am relating this to democracy which is my topic of design... see if external forces start interfearing in the matters of a democratic state... unstability occures in that state just like gases

I'm still not sure of what you're looking for exactly.
As said before, helium molecules move randomly in a 3D model.

I'll add that the speed of a helium molecule at 25 degrees Celsius is 1.23 x 10^3 m/s.

Increasing the temperature will increase the speed.

And finally, I cannot see in any way how you link democracy or architecture to helium molecules. Maybe I'm too young for that...

my question is what is the movement of Helium Molecule...and i am associating the idea of change in the speed at which the molecules of noble gases if applied external force like heat....i am relating this to democracy which is my topic of design....see if external forces start interfearing in the matters of a democratic state...unstability occures in that state just like gases

So you are looking for a metaphor for "heating" a democracy?

Heat just makes all the molecules move faster. So chemical reactions tend to happen faster. (And of course, proteins are often denatured, so they don't work properly at high temperatures. But that's unrelated to gases being heated.)

In contrast, enzymes work like an external force to speed up specific reactions but not others.

Hope this helps!