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Shapes and size of orbitals

Shapes and size of orbitals

An orbital is a region of space around the nucleus where the probability of finding an electron is maximum. This probability is around 90 to 95%.

The shape of this region which is also called as electron cloud gives the shape of an orbital. This shape is determined with the help of Azimuthal quantum number, however, the orientation of orbital in space is given by magnetic quantum number.




Shapes of various orbitals have been discussed below:

s – Orbital:

s-orbital are spherical and symmetrical about the nucleus and the probability of finding the electron goes on decreasing as one move away from nucleus i.e. probability of finding the electron in s orbital is maximum near the nucleus and decreases as one move far from the nucleus. For s orbital the value of Azimuthal Quantum Number ‘l’ is 0 and hence the possible value of magnetic quantum number m = 0 only and it indicates that s orbital has only one possible orientation in space.

A node is a place where the probability of finding the electron is zero.

There is no radial node in 1s orbital however, there is a vacant space between two successive vacant orbitals which we termed as the radial node and hence 2s orbital has a radial node.

Similarly, we can say that for an s orbital with principal quantum number ‘n’ number of radial nodes will be ‘n-1’.

shape of s orbital

The size of orbitals depends upon the value o the principal quantum number. Greater the value of n, larger is the size of the orbital. Hence, 2s-orbital is larger than 1s-orbital however both the orbitals are non-directional and spherically symmetrical in shape.

 

p – Orbital:

The shape of p-orbitals is similar to a dumb-bell.  The probability of finding an electron is maximum in the two lobes on the opposite side of the nucleus. The value of Azimuthal quantum number ‘l’ for p orbital is 1.

For l = 1, possible value of magnetic quantum number, m are -1, 0 and +1.

Hence, p orbital has three different orientation in space which are designated as px, py and pz depending upon the density of electron is maximum along the x y and z axis respectively.

The p orbital is not symmetrical and hence there arises directional character and also the two lobes of p orbital are separated by a nodal plane.

shape of p orbital

The three p-orbitals belonging to a particular energy shell have equal energies and are called degenerate orbitals.

 

d – Orbital:

The value of Azimuthal quantum number ‘l’ for d orbital is 2.

For l = 2, possible value of magnetic quantum number, m are -2, -1, 0 and +1, +2.

Hence, d orbital has five different orientation in space which are designated as  dxy, dyz, dzx,  dz2 and dx2– y2.

The geometry of d-orbital is complex and is shown below.

shape of d orbital

Orbitals dxy, dyz, dzx are projected between the axis whereas the other two orbitals viz. dz2 and dx2– y2 lies along the axis.




 

Nodes in orbitals:

 

Generally, two types of nodes are found in orbitals viz. angular nodes and radial nodes. The angular nodes in an orbital are determined by the Azimuthal quantum number ‘l’. Angular nodes are the flat planes found at fixes angles.

The total number of nodes present in an orbital = n-1

The quantum number ‘l’ denotes the number of angular nodes, so

Total radial nodes for an orbital will be N = n – l – 1

For example,  to determine the nodes in the 4px orbital, given that n = 4 and ℓ = 1 (because it is a p orbital). The total number of nodes present in this orbital is equal to n-1. In this case, 4-1=3, so there are 3 node. The quantum number ℓ determines the number of angular nodes; there is 1 angular node, specifically on the yz  plane because this is a px orbital. Now, there are two nodes left, there must be two radial nodes. To sum up, the 4px orbital has 3 nodes: 1 angular node and 2 radial node.

The number of radial and angular nodes can only be calculated if the principle quantum number, type of orbital (s,p,d,f), and the plane that the orbital is resting on (x,y,z, xy, etc.) are known.

 

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About Utkarsh Gupta

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