Uranium has two isotopes of masses 235 and 238 units. If both are present in uranium hexa fluoride gas, which would have the larger average speed ? If atomic mass of fluorine is 19 units, estimate the percentage difference in speed at any temperature.

Explanation

At a fixed temperature the average energy `= 1//2 m v^(2)`
` is constant. So smaller the mass of the molecule, faster will be the speed. The ratio of speeds is inversely proportional to the square root of the ratio of the masses. The masses are 349 and 352 units. So
`V_(349)// V_(352)= (352// 349)^(1//2) = 1.0044` . Hence difference `(DeltaV)/(V) = 0.44 %`. = [`""^(235)U,` is the isotope needed for nuclear fission. To separate it from the more abundant isotope `""^(238)U`, the mixture is surrounded by a porous cylinder. The porous cylinder must be thick and narrow, so that the molecule wanders through individually, colliding with the walls of the long pore. The faster molecule will leak out more than the slower one and so there is more of the lighter molecule (enrichment) outside the porous cylinder . The method is not very efficient and has to be repeated several times for sufficient enrichment.)