he average value of the radiusrfor a radial functionRn, l(r) of a hydrogen-like atom is〈r〉=∫R∗n, l(r)rRn, l(r)dτ=∫[infinity]0R∗n, l(r)rRn, l(r)r2dr.(1)The most probable value of the radiusrmpis located whereddr(r2Rn, l(r)2)= 0.(2)Calculate〈r〉andrmpfor a hydrogen-like atom with chargeZin the 1s and 2s states. Youwill find the necessary integral andRn, l(r) formulas on the equation sheet. You may usenumerical software or your graphing calculator to find the roots of the cubic polynomial thatyou should get when findingrmpfor the 2s state. Take the largest root asrmp.