A Radial Probability Distribution of Apples Distance from trunk 2.3.2 The radial distribution function The probability of finding electron in the region of space r dr,0 d0,p dp dr=r2sin edrdedo lv'dr =[R (ry"(0.)r'sin Odrd@do .What is the probability of electron at r dr,(in a thin spherical shell centered at the origin)? R(rrdrf"fy"(0.o) sinededo=r2R2(r)dr Normalized spherical harmonics D=2R2(r) Radial distribution functionA Radial Probability Distribution of Apples 2.3.2 The radial distribution function • The probability of finding electron in the region of space r + dr, θ + dθ, φ + dφ ψ dτ [ ] R r Y θ ϕ r θdrdθdϕ m nl l ( ) ( , ) sin 2 2 2 2 = R r r dr Y d d r R r dr nl nl m l ( ) ( , ) sin ( ) 2 2 2 0 2 0 2 2 = ∫ ∫ θ ϕ θ θ ϕ π π Normalized spherical harmonics ( ) 2 2 D r R r nl = Radial distribution function dτ r sin θdrdθdϕ 2 = •What is the probability of electron at r + dr,(in a thin spherical shell centered at the origin)?