Question

3.27 Average distance from the nucleus and atomic radius The maximum in the radial probability distribution of an electron in a hydrogen-like atom is given by Equation 3.58, that is, rmax - (n'ao)/Z, for l - n- 1. The average distance F of an electron from the nucleus can be calculated by using the definition of an average and the probability distribution function Pn/(r), that is, Z. elective 2 2n2 in which the right-hand side represents the result of the integration (which has been done by physicists). Consider the two inert gases Ne and Ar that have outer electronic configurations 2p6 and 3p6. The ionization energy of Ne is 21.6 eV whereas for Ar it is 15.8 eV. Use the ionization energy to calculate an Zeffective for each atom, and then use this Zeffective to estimate the average radius of the atom. Viscosity measurements on these gases interpreted by assuming a hard sphere model for atoms indicate 0.14 nm for He and 0.17 nm for Ar (from Y. Zhang and Z. Xu, American Mineralogist, 80, 670, 1995.)

Answer 1