The document discusses the shapes of atomic orbitals. It explains that electron clouds are not uniform but densest where electrons are most likely to be found. S orbitals are spherical around the nucleus, with larger orbitals having higher principal quantum numbers n. P orbitals have a dumbbell shape with three orientations (px, py, pz) at right angles. D orbitals consist of five shapes, two along the axes and three between the axes, with differing probability distributions.

1. SHAPE OF ORBITALS According to modern concept, electron has properties both of particles and wave. Electron is actually not a dot (as usually represented) but seems like a cloud. The shape of electron cloud is the shape of the orbital in which it is present. Electron cloud is not uniform but is dense where the probability of finding the electron is maximum.

2. The s orbitals are spherically symmetrical about the nucleus. Their size increases with the increase in the value of n. Thus 2s (n=2) orbital is larger than the 1s orbital (n=1) but smaller than the 3s orbital (n=3). There is a region between every two adjacent s orbitals where the probability of finding an electron is zero (node). Being spherical, s orbitals are non-directional.

3. Y 1S 2S + X NODE Z

4. The p orbitals consist of two lobes to form dumb-bell structure. Since in the p sub-level there are three orientations, there are three p orbitals: one lying along the X-axis, the second along Y-axis and the third along Z-axis. These are respectively termed as px , py and pzorbitals; these lie at right angle to each other. Y X pyorbital pyorbital pz orbital Z

5. Thus while s orbitals are non-directional, p orbitals have a directional character. All the p orbitals of a particular shell have same energy (degenerate orbitals). The p orbitals of higher energy levels (n=3, 4, 5,,…..) have similar shapes although their sizes are bigger. The two lobes of a p orbital are separated by a nodal plane, i.e. plane of zero electron density.

6. The d sub-shell, which can accommodate 10 electrons, can be resolved into five orbitals. The five d orbitals of a sub-shell possess equal energy and differ only in their orientations in three dimensional spaces. X Z Y X X Y d z2 d x2 - y2 Z Z Y dxy dxz dyz

7. The following significant features of the shape of d orbitals must be noted: The first two orbitals lie along the co-ordinate axes (d z2 is lying along the Z axes while d x2 – y2 is lying along X and Y axes). Thus they have their maximum electron probable density along their respective axes i.e. Z in d z2 and X and Y in d x2 – y2 . The other three orbitals project in between the co-ordinate axes. These, designated as dxy , dyz and dxz, have their probability maxima lying along lines that make 45° around with the axes. The dx2 - y2 orbital is exactly like dxy orbital except that a rotation of 45° around the z-axis gives it lobes which are directed along the axis.