Chapter 1st
B.sc 1st year Book
(Page 6)

Shapes of orbital

s-orbital : There is one s-orbital in every principal shell. Each s-orbitals is spherically symmetrical because their electron density is not concentrated along any particular directions . This orbital has the following characteristic properties:
(i) It can have only one possible orientation:
(ii) All s – orbitals are similar in shape but become larger in size with the higher value of

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(ii) 1 s orbital is surrounded by 2 s – orbital, 2 s – orbital is surrounded by 3 s – orbital and 90 on.
(iv) There is a region between two adjacent s – orbitals where the probability of binding an electron is zero. This is called ‘nodal plane’ or ‘nodal surface’. The s-orbitals other than 15 are more complicated as they contain nodal surfaces. The number of nodal surfaces is . It the nodal surface is (n-1) at infinity is excluded

Shapes of 1s,2s and 3s arbitalsp-orbitals : Each principal shell has a set of three p-orbitals (except K-shell), In p-orbitals the probability of finding an electron is more in some particular directions from the nucleus. The probability distribution diagram of p-orbital shows that this orbital consists of two lobes one on each side of the nucleus i.e. it is dumb-bell in shape. The p-orbitals have the following characteristic properties:
(i) The probability of finding an electron is equal in both side of the nucleus in the lobes.
(ii) Depending upon the orientation, p-orbitals have been denoted as px, py and pz because their lobes of maximum electron density lie along x, y and z axes in space respectively.
(iii) All these orbitals have identical energies but different identifies as individuals.
In other words in the absence of applied magnetic field the p orbitals are equivalent in energies and said to be triply or three- fold degenerate.
(iv) When these orbital visualize collectively they appear as concentrically spherical around the origin of the cartesian axes.
(v) The p-orbitals have a plane of zero electron density referred to as nodal plane which separate the two lobes e.g. xy plane is the nodal plane of pz-orbital.

Shape of 2p orbitals of the hydrogen atom.d-orbitals : Each principal shell (except K and L shells) has a sell of five d-orbitals which have the same radial function but differ in angular distribution. Structurally d-orbitals are of two types:
(a) The orbitals with double dumb-bell shaped for example : dxy, dyz, dxz and orbitals have the same shape but differ in their orientation orbitals.
(b) The orbital of a dumb-bell shape with a collar for example : orbital.
Depending upon the orientation of orbitals in three dimensional space d-orbitals are further divided into two groups e.g.
(i) The orbitals which have their lobes in between two adjacent axes, making  with the axes. For example : dxy, dyz and dxz orbitals because they lie in xy, yz and xz planes respectively. A set of these orbitals is called ‘triply’ degenerate ‘  ‘ set.
(ii) The orbitals which have their lobes along the axis/axes tor example orbitals have the same shape but differ in their orientation orbitals have their lobes along x and y cartesian axes and orbital has its lobes along z. axis. Both these orbitals are collectively known as ‘doubly’ degenerate ‘eg’ set.

The characteristic properties of d-orbitals are :

1.set of orbitals have two nodal planes each.
2. The orbital contains two cone shaped nodal surfaces. Thus, this orbital is different from the other four d-orbitals viz. dxy, dyz, dxz and orbitals have the same shape but differ in their orientationorbitals. It is because most of its density is concentrated around the z-axis.
3. In absence of magnetic field, all the five d-orbitals are equivalent in energies and are called “five – fold degenerate’, but in the presence of magnetic field d-orbitals split into two sets of orbitals sets:
Shape of d-orbitals of the hydrogen atom

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