Orbitals dumb-bell

Ap subshell contains three p orbitals, denoted px, py and pz. A p orbital is a dumb-bell shape. 

The wavefunction of an electron associated with an atomic nucleus. The orbital is typically depicted as a three-dimensional electron density cloud. If an electron s azimuthal quantum number (/) is zero, then the atomic orbital is called an s orbital and the electron density graph is spherically symmetric. If I is one, there are three spatially distinct orbitals, all referred to as p orbitals, having a dumb-bell shape with a node in the center where the probability of finding the electron is extremely small. (Note For relativistic considerations, the probability of an electron residing at the node cannot be zero.) Electrons having a quantum number I equal to two are associated with d orbitals. 

Orbitals. Atomic orbitals represent the angular distribution of electron density about a nucleus. The shapes and energies of these amplitude probability functions are obtained as solutions to the Schrodinger wave equation. Corresponding to a given principal quantum number, for example n = 3, there are one 3s, three 3p and five 3d orbitals. The s orbitals are spherical, the p orbitals are dumb-bell shaped and the d orbitals crossed dumb-bell shaped. Each orbital can accomodate two electrons spinning in opposite directions, so that the d orbitals may contain up to ten electrons. 

Each of the sp3 hybridised orbitals has the same shape. This deformed dumb-bell looks more like a p orbital than an s orbital since more p orbitals were involved in the mixing process, i.e. one lobe is larger as compared to other lobe ... 

The deformed dumb-bell shapes permit a better orbital overlap than would be obtained from a pure s orbital or a pure p orbital. A <7bond between an sp3hybridised carbon atom and a hydrogen atom involves the carbon atom using one of its half-filled sp3 orbitals and the hydrogen atom using its half-filled Is orbital. 

The unhybridised 2py orbital has the usual dumb-bell shape. Each of the sp2 hybridised orbitals has a deformed dumb-bell shape similar to an sp3 hybridised orbital. The difference between the sizes of the major and minor lobes is larger for the sp2 hybridised orbital than that in case of sp3 hybridised orbitals. 

The sp hybridised orbitals are deformed dumb-bells with one lobe much larger than the other. The 2py and 2pz orbitals are at right angles to each other. The sp hybridised orbitals occupy the space left over and are in the xaxis pointing in opposite directions (only the major lobe of the sp orbitals are shown in black in following figure (b)). 

For a spherically symmetrical wave function of an electron in an s state (s orbital, s wave function) there is naturally no preferred direction. This is, however, quite otherwise for a p orbital which, as explained, has as far as the angular dependence is concerned the shape of a dumb bell consisting of two spheres on one another, directed along the x>y or z axis (Fig. 11). The charge distribution, cp 2, has the shape of a figure 8. 

Orbitals are the regions in space that the electrons are said to frequent, and s-orbitals are spherical. p-Orbitals are shaped like dumb-bells, as shown in Figure 2.2.10. 

For practical reasons, various graphical representations of atomic orbitals are used. The most useful are boundary surfaces, such as those shown in Figure 2. These enclose regions of space where the electron described by the corresponding wave function (orbital) can be fotmd with high probability (e.g., 99%) s orbitals are spherical, p orbitals are dumb-bell shaped, d orbitals have a four-leaf-clover shape, while/orbitals have complex shapes. 

Atomic Orbitals Carbon has six electrons, i.e. and is placed in second period of the periodic table. In it there are two shells of atomic orbitals available for these electrons. The first shell closest to the nucleus has a single 5 orbital-the Is orbital. The second shell has a single s orbital (the 2s orbital) and three p orbitals (3 2p). Therefore, there are a total of five atomic orbitals into which these six electrons can fit. The s orbitals are spherical in shape with the 2s orbital being much larger than the Is orbital. The p orbitals are dumb-bell-shaped and are aligned along the x, y and z axes. Therefore, they are... 

Similarly, orbitals containing p electrons are termed p orbitals. There are three types of p orbital (labelled p and pj, which are normally of equal energy but which have different directions in space. The shape of a p orbital is often described as a dumb-bell (Fig. 3.13). Orbitals containing d electrons are termed d orbitals. There are five types of d orbitals, and each is normally of equal energy. The shape of d orbitals is complicated and will not concern us here. 

GaSe, shown in Figure 3, has a iayer structure with a very pronounced cieavage between the layers. The Ga atoms form dumb-bells. The non-bonding orbitals on the Se atoms are directed towards the space between the layers. 

The p orbitals have two lobes forming a dumb-bell shape and have different orientations in space. They are arranged at right angles to each other and are labelled p, p and p to reflect their orientation. The three p orbitals all have the same energy - the orbitals are said to be degenerate. The 3p orbitals have the same shape as the 2p orbitals but are larger. 

The p orbitals have a dumb-bell shape. The three p orbitals are arranged along the x, y and z axes in space. Figure 2.57 shows three p orbitals of an atom. The sizes of the p orbitals are 2p < 3p < 4p. There is no Ip orbital. 

FIGURE 5.7 A p orbital has two regions of high probability, which gives a dumb-bell shape, (a) Each p orbital is aligned along a different axis from the other p orbitals. 

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