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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]