Shapes of s p and d Orbitals | Atomic Orbital | Chemistry Videos
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Shapes of orbitals : An
Shapes of orbitals : An orbital is the region of space around the nucleus within which the probability of finding an electron of given energy is maximum. The shape of this region (electron cloud) gives the shape of the orbital. Observe carefully the shape of S, P and D orbital.
Shape of s-orbitals : It may be noted that one S orbital the probability density is maximum at the nucleus and it decreases sharply as we remove as from it. On the other hand for two S orbital the probability density first decreases sharply to zero and again starts increasing. After reaching a small maxima it decreases again and approaches zero as the value of R increases further. The region where this probability function reduces is called nodal surfaces or simply nodes. In general it has been found that NS orbital has N minus one nodes. That is the number of nodes increases with increase of principle number N. In other words the number of nodes for two S orbital is one, two for three S orbital and so on. These probability density variations can be visualized in terms of charged cloud diagrams. In these diagrams the density of the dots in region represents the electron probability density in that region.
Bounded surface diagrams of constant probability density for different orbitals give a fairly good representation of the shapes of the orbital. In this representation a boundary surface or contour surface is shown in space per orbital on which the value of the probability density is Psi square is constant. In principle many such boundary surfaces must be possible. However for a given orbital only that boundary surface diagram of constant probability density is taken to be the good representation of the shape of the orbital which includes a region of the volume in which the probability of the finding the electron is very high. Say around 90 percent one may ask why do we not go the boundary surface diagram which bounces a region in which the probability of finding the electron is 100 percent. The answer to this question is that the probability density Psi square has always have some value however so it may be any final distance from the nucleus. It is therefore not possible to draw boundary surface diagrams of rigid size in which the probability of finding the electron is 100 percent.
Boundary surface diagram from S orbital is actually a spear center on the nucleus. In two dimension, this spear looks like a circle. It encloses a region in which a probability of finding the electron is about 90 percent. Thus we see that one S and two S orbitals are spherical in shape. In reality all those S orbitals are spherically symmetry. That is the probability of finding the electron at a given distance is equal in all the directions. It is also observe that the size of the S orbital increases with increase in N. That is the size of the four S orbital is greater than the size of the three S orbital which is greater than that of the two S orbital which is greater than that of the one S orbital. And the electron is located further away from the nucleus as the principle quantum number increases.
Shape of p-orbitals : For p-subshell L is equal to one, there are three values of m namely -1, 0, +1. It means that p orbitals can have three possible orientations. These three p-orbitals are equal in energy (degenerate state) but differ in their orientations. Each p-orbital consists of two lobes symmetrical about a particular axis. Depending upon the orientation of the lobes, these are denoted as 2pX , 2pY and 2pZ accordingly as they are symmetrical about X,Y and Z - axis respectively.
The lines in the figure represents the cross-section of the three dimensional boundary surface of p-orbitals. The boundary surface means the surface which encloses 90 percent of the dots representing the electrons. Two lobes of each p orbital are separated by a nodal plane (a plane having zero electron density). For example, for 2pX orbital, YZ plane is the nodal plane X.
Thus, p-orbitals have dumb-bell shape and have directional character. The probability of finding the electron is equal in both the lobes. The p-orbitals of higher energy levels have similar shapes although their size are bigger.
Shape of d-orbitals : For d-subshell, L is equal to Two, there are five values of m namely2, -1, 0, 1, 2. It means d-orbitals can have five orientations. These are represented by dXY, dX square dYsquare, dZX, dZ square and dYZ; for example, 3dXY, 3dYZ, 3dZX, 3dX square minus Y square and 3dZ square. The dXY, dYZ and dZX orbitals have same shape i.e., clover leaf shape but they lie in XY, YZ and ZX planes respectively.The dZ square orbital is symmetrical about Z-axis and has a dumb - bell shape with a doughnut shaped electron cloud in the centre. The dX square minus Y square orbital is also clovar leaf shaped but its leaves are directed along the X and Y axis.
Shape of s-orbitals : It may be noted that one S orbital the probability density is maximum at the nucleus and it decreases sharply as we remove as from it. On the other hand for two S orbital the probability density first decreases sharply to zero and again starts increasing. After reaching a small maxima it decreases again and approaches zero as the value of R increases further. The region where this probability function reduces is called nodal surfaces or simply nodes. In general it has been found that NS orbital has N minus one nodes. That is the number of nodes increases with increase of principle number N. In other words the number of nodes for two S orbital is one, two for three S orbital and so on. These probability density variations can be visualized in terms of charged cloud diagrams. In these diagrams the density of the dots in region represents the electron probability density in that region.
Bounded surface diagrams of constant probability density for different orbitals give a fairly good representation of the shapes of the orbital. In this representation a boundary surface or contour surface is shown in space per orbital on which the value of the probability density is Psi square is constant. In principle many such boundary surfaces must be possible. However for a given orbital only that boundary surface diagram of constant probability density is taken to be the good representation of the shape of the orbital which includes a region of the volume in which the probability of the finding the electron is very high. Say around 90 percent one may ask why do we not go the boundary surface diagram which bounces a region in which the probability of finding the electron is 100 percent. The answer to this question is that the probability density Psi square has always have some value however so it may be any final distance from the nucleus. It is therefore not possible to draw boundary surface diagrams of rigid size in which the probability of finding the electron is 100 percent.
Boundary surface diagram from S orbital is actually a spear center on the nucleus. In two dimension, this spear looks like a circle. It encloses a region in which a probability of finding the electron is about 90 percent. Thus we see that one S and two S orbitals are spherical in shape. In reality all those S orbitals are spherically symmetry. That is the probability of finding the electron at a given distance is equal in all the directions. It is also observe that the size of the S orbital increases with increase in N. That is the size of the four S orbital is greater than the size of the three S orbital which is greater than that of the two S orbital which is greater than that of the one S orbital. And the electron is located further away from the nucleus as the principle quantum number increases.
Shape of p-orbitals : For p-subshell L is equal to one, there are three values of m namely -1, 0, +1. It means that p orbitals can have three possible orientations. These three p-orbitals are equal in energy (degenerate state) but differ in their orientations. Each p-orbital consists of two lobes symmetrical about a particular axis. Depending upon the orientation of the lobes, these are denoted as 2pX , 2pY and 2pZ accordingly as they are symmetrical about X,Y and Z - axis respectively.
The lines in the figure represents the cross-section of the three dimensional boundary surface of p-orbitals. The boundary surface means the surface which encloses 90 percent of the dots representing the electrons. Two lobes of each p orbital are separated by a nodal plane (a plane having zero electron density). For example, for 2pX orbital, YZ plane is the nodal plane X.
Thus, p-orbitals have dumb-bell shape and have directional character. The probability of finding the electron is equal in both the lobes. The p-orbitals of higher energy levels have similar shapes although their size are bigger.
Shape of d-orbitals : For d-subshell, L is equal to Two, there are five values of m namely
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