Atoms root mean square velocity

Calculate the root mean square velocity for the atoms In a sample of helium gas at 25°C. Solution... 

The escape velocity necessary for objects to leave the gravitational field of the Earth is 11.2 km Calculate the ratio of the escape velocity to the root-mean-square speed of helium, argon, and xenon atoms at 2000 K. Does your result help explain the low abundance of the light gas helium in the atmosphere Explain. 

MD simulations have been employed in a wide variety of simulations. In the simplest applications, trajectories are generated for biomolecular systems and analyzed for a variety of structural, dynamic, and thermodynamic properties. The average motions of atoms over time may be observed, as well as time correlations for atomic positions and velocities. This type of information can often provide insight regarding structure-function relations and mechanistic details for biomacromolecules. Root mean square position fluctuations and other rms geometric fluctuations can be computed and compared with experimental observations. For example, in the limit of harmonic and isotropic atomic motion, mean square position fluctuations... 

Use the graph of G(v) from exercise 19.72 to determine what percentage of atoms have a velocity within 1% of (a) the root-mean-square speed (b) the most probable speed and (c) the mean speed. Are the percentages similar ... 

Note that since mobility and conductivity, which are material properties, depend on the collision time, then this collision time must be independent of the applied field if Ohm s law is to be obeyed. Why should the collision time be a material property The mean free path for electrons to travel before collisions would seem fo be a much more reasonable material property since it is determined by the size and number density of atoms in the structure. But the mean free path A is the velocity times the collision time t and since i>d is directly proportional to tE, the collision time would be inversely proportional to the square root of the field, in violation of Ohm s law. This paradox can be resolved (at least temporarily) by assuming that the thermal velocities of the electrons are much higher than i>d so that A = r(i th d) I t th- Let us now check to see if this assumption is valid. 

---