## Atomic Radius

Imagine an ideal gas, for example hydrogen, contained in a container of volume V, which has a temperature T and exerts a pressure on the same P. With the aim of the radio anlizar hydrogen atoms with the average velocity of its molecules, the following will Desarrolo below: From PV = nRT, mam dividing by Avogadro's num N: PV / N = nRT / N, the term V / N = a , would the apparent volume of a molecule if we neglect the average distance between these: PA = nkT, where K = R / N, Boltzmann constant. If concideramos atomic volume, a / 2 = Q, where Q is the preload of the hydrogen atom, therefore, PQ = NkT / 2. Solving for T, T = 2PQ/nK. Given the equation of the kinetic-molecular theory of gases: T = IU * 2.M/3R, IU * 2 is the mean square speed of the molecule and M is the molar mass. T Equating the last two equations: ui2.M/3R = 2PQ/nK, solving and simplifying is: IU * 2.m / P = 6Q. The hydrogen atom orbital is spherical symmetry, so that Q = 4 (pi) r * 3 / 3. Replacing: IU * 2.m / P = 8 (pi) r * 3, where m is the unit mass of a proton, and r is the atomic radius of spherical symmetry (for a quantum level n = 1). Solving Re is: Re = (ui * 2.m / 8 (pi) P) * (1 / 3), allowing to calculate the atomic radius root of the average velocity of the gas. These results show that, depending on the energetic state of the particles may be variations in the relative distances of electron-proton in the hydrogen atom, ie the orbital energy is not constant, but varies depending on the thermal and kinetic state of its neighboring molecules.