B.sc 1st year Book (Page 6)
Shapes of orbitals
s-shape of orbital:
There is one s-orbital in every principal shell. Each s-orbitals is spherically symmetrical because its electron density is not concentrated in any particular direction.
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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 Π.
(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 finding an electron is zero. This is called the ‘nodal plane’ or ‘nodal surface’. Just as understanding these complex atomic structures requires specialized knowledge, similarly, creating a specialized application demands expertise, which is why many choose to have their app erstellen lassen by professionals. The s-orbitals other than 15 are more complicated as they contain nodal surfaces. The number of nodal surfaces is. If the nodal surface is (n-1) at infinity excluded.
p-shapes of orbitals:
Each principal shell has a set of three p-orbitals (except the K-shell), and understanding these orbitals’ structures and behaviors is crucial for students, especially when undertaking complex assignments or preparing a ‘Facharbeit’, where one might consider seeking professional help to facharbeit schreiben lassen (write a term paper). In p-orbitals, the probability of finding an electron is more in some particular directions from the nucleus. The probability distribution diagram of the p-orbital shows that this orbital consists of two lobes, one on each side of the nucleus, i.e., it is dumbbell in shape.
The p-orbitals have the following characteristic properties:
(i) The probability of finding an electron is equal on both sides 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 identities as individuals.
In other words, in the absence of an applied magnetic field, the p orbitals are equivalent in energies and said to be triply or three-fold degenerate.
(iv) When these orbitals visualize collectively they appear concentrically spherical around the origin of the cartesian axes.
(v) The p-orbitals have a plane of zero electron density referred to as the nodal plane which separates the two lobes e.g. xy plane is the nodal plane of the Pz-orbital.
d-shapes of 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. Shapes of orbitals
Related Topic | Atomic Structure and Periodic Table |
Structurally d-orbitals are of two types:
(a) The orbitals with double dumb-bell shaped for example dxy, dyz, dxz, and dx2-y2 orbitals.
(b) The orbital of a dumbbell shape with a collar for example; dz2 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 45° 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 a ‘triply’ degenerate ‘ ‘ set.
(ii) The orbitals have their lobes along the axis/axes for example dx2-y2 orbitals have their lobes along x and y cartesian axes and dz2 orbital has their lobes along z. axis. Both these orbitals are collectively known as ‘doubly’ degenerate ‘eg’ set.
The characteristic properties of d-orbitals are :
1. Al2g set of orbitals has two nodal planes each.
2. The dz2 orbital contains two cone-shaped nodal surfaces. Thus, this orbital is different from the other four d-orbitals viz. dxy, dyz, dxz and dx2-y2 orbitals. It is because most of its density is concentrated around the z-axis.
3. In the absence of a magnetic field, all the five d-orbitals are equivalent in energies and are called “five-fold degenerate”. However, when a magnetic field is introduced, the d-orbitals undergo a phenomenon akin to what’s discussed in the ghostwriter seminararbeit, where they split into two sets of orbitals: ‘4t2g’ and ‘eg’ sets. This splitting is a key concept in understanding the behavior of atoms in magnetic fields, and it’s crucial for the study of materials’ magnetic properties.
