Question

The most chemically important orbitals are s, p, and d orbitals. Provide sketches or plots for 4s, 4p and 4d orbitals of the angular portion pf the wave function, the radial portion of the wave function and the radial probability distribution. Clearly identify all the nodes in these images and list the physical importance of these nodes. Then combine this information to provide complete images of these orbitals.

Answer 1

Nodes Angular nodes Radial nodes n-2- 4-0-153 - uso - 46 ud ooro 4-1-152 4-2-1= 1 node tet is a point at which enction cuts a-asus, other then boundary conditions. 45 no angular mode, only Radial nodes 45 ano. of Radial noder a3, hence graph will cut a-asus 3 time shape of angular nodes

- 45 - nooof Radial nodes=3 , hence graph will cert a-asus 3 times. - shape of Radial noder 1 Wh n - the sign of ware fonction changes around a node on reporrent Radial nodes Region 0, 2, 3 Referent Radial node Radial Probability distributions fonction us does not contain angular node 2*uh s(pm) hence shape od us i all s-orbitals are inspherical shape 46 number of angulan nades no of airean nodes 1 =2 shape chup-nodes 4(x) 12 Represent Radial nodes.

angular node in uporbital fet 4px a them & ga plane will Repocsent angulon node 1793-plare Cangular nede) tall p-orbital are dembell shape. . to 4d orbital angular nodes , Radial nodes 22 I 1 I graph will cut acasus 2 anyonce shape of Radial nodes Up(x) 1 Represent Radial a nodes Angulan node I arra Im a angular nodes - all d-orbital are double-dombell shape