Question

(IV) Explain/answer the following questions without actually performing any calculation: A Argue why the total energy eigenfunctions for H atom are not eigenfunctions of the kinetic energy operator? B Consider 3s, 3p, and 3d orbitals that you know from the general chemistry classes which correspond to angular momentum quantum numbers I = 0,1, and 2. Write down the total potential V which contains the sum of the Coulomb and centrifugal potentials. (Hint: see the slides for Chapter 7 " Quantum mechanical description of the hydrogen atom") C Look at the radial density for the ls orbital weighted by r?; the maximum is found at the distance of lao 0.529177A. zlash Distance from nucleus () What is the effect of the centrifugal potential on the radial density r2|(r)l2 for 3s 3p, and 3d orbitals? Where would you expect the maximum of r? (r) in each case?

Answer 1

A). As we know hydrogen atom consist of one electron and one proton in which electron moves aroumd the nucleus (classically) and in form of electron cloud (quantum mechanically). The total energy will be kinetic energy only and olny if particle is free (i.e, No force acts upon it) But im hydogen atom there is colombic force by the proton which acts upon electron so there is also coloumbic potential energy (which is negative due to negative charge on electron) present in total energy hence eigen function will not be only of kinetic energy operator only.

B).