14. (a) The equation below is the radial Schrödinger wave equation for the hydrogen atom. Without going into full mathem

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14 A The Equation Below Is The Radial Schrodinger Wave Equation For The Hydrogen Atom Without Going Into Full Mathem 1 (41.75 KiB) Viewed 37 times

14. (a) The equation below is the radial Schrödinger wave equation for the hydrogen atom. Without going into full mathematical detail, explain how this equation is obtained from the full three-dimensional Schrödinger wave equation. d²R 2dR 2u dr² r dr ħ² (E+) 1(1+1)ħ² R=0 4πέν 2μr² [7] (b) Explain what each of the terms inside the brackets represent and how the quantum number / is related to the orbital angular momentum of the electron. [5] (c) The radial wave function for an electron in the first excited state is given by R(r) = Ar e=¹/b where A and b are constants. Calculate the most probable and the average dis- tances of the electron from the proton. [Note:Jox" exp(-Kx) dx = n!/K"+¹] [8]