Question

The 3s orbital has two radial nodes. Radial nodes occur at Rn,l(r) = 0. Determine the values r for those nodes in terms of a0. (Hint: Focus on the quadratic equation in the parentheses only and solve it for ρ. Thus the roots or the two values are yielded for ρ. Continue on to solve for r twice using ρ = (2Z/na0)r.)

Answer 1

a Radial ware function for as-arbital Rus · Il p2-6P+6) 2-82 913 for R3s P? = 0, 6P + Ő = 0. r Qx2+bx+c 7 Bett L X=-bI56²-4ac Similarly za p= -b II 62_49 2a b = -6 <= 6 a = q . 6 Į Į 36-24 2 8 = -(-6) 1 11-62 - 4x06 = 2. Pe 6255 pa 3+ 13. Se 3+ So = f. a 22 Y nao EL 22r 300 as, n=3 n = 3 y = 3(3+ 3) ao 2zV 2z 39. V = 0 g + 353 aoi 2 z