An orbital is the region of space around the nucleus within which the probability of finding an electron of given energy is maximum (about 90%). The probability at any point around the nucleus is calculated using Schrodinger wave equation and is represented by the density of the points. The shape of electron cloud thus obtained gives the shape of the orbital.
Shapes of s-Orbitals :- As we know that the co-ordinates (x, y, z) of the electron with respect to the nucleus, Schrodinger wave equation can be solved to get the value of the orbital wave function ¥. But ¥ has no physical significance. Instead, the square of its absolute value, i.e square of ¥ has the significance as it gives the electron probability density of the electron at the point.
Thus, we observe that the probability of 1s electron is found to be maximum near the nucleus and decreases as the distance from the nucleus increases. In case of 2s electrons, the probability is again maximum near the nucleus and then decreases to zero and increases again and then decreases as the distance from the nucleus increases. The intermediate region (a spherical shell) where the probability is zero is called a nodal surface or simply node.
Shapes of p-Orbitals :- On the basis of probability calculations, it is found that the probability of finding the p-electrons is maximum in two lobes on the opposite sides of the nucleus. This gives rise to dumb-bell shape of the p-orbital. However, it may be noted that the probability of finding a particular p-electron is equal in both the lobes. Further, there is a plane passing through the nucleus on which the probability of finding the electron is almost zero. This is called a nodal plane.
Shapes of d-Orbitals :- There are five d-orbitals. Depending upon the axes along which or between which their electron clouds are concentrated , note that d-orbital has a doughnut-shaped electron cloud in the centre whereas others have clover leaf shape. Further 3d has no node, 4d has one, 5d has two, and so on.
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