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Atomic Orbitals: Shapes And Energies

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Atomic Orbitals: Shapes And Energies - Lesson Summary

The three-dimensional space around the nucleus where the probability of finding the electron is maximum, called orbital. The probability of finding an electron is a function of distance (r) from the nucleus. The probability of finding an electron at a distance from the nucleus is called Radial probability distribution.

The region where the probability density function reduces to zero is called radial nodes or Nodal surfaces or nodes. For s orbitals, the number of radial nodes increases with the value of the principal quantum number n, and found to be equal to n - 1.

The shape of the electron cloud density and that of boundary surface determines the shape of the orbital. The boundary surface diagram for s orbital is always a sphere centred on the nucleus, irrespective of the principal shell.

The boundary surface diagram for the p orbital indicates the presence of two lobes that lie on either side of the plane that passes through the nucleus, giving a dumb-bell shape to the p orbital.

The shape suggests that the probability of finding the p-electrons is the maximum within the two lobes.

In p orbitals also, increase in size and energy with increase in the principal quantum number. The number of radial nodes for p orbitals is given by the expression (n - 2); therefore, number of radial nodes is zero for 2p orbital, one for 3p orbital, two for 4p orbital.

The probability density function is zero on the plane where the two lobes touch each other. The shape of d orbital is double dumb-bell. And energy increases with increase in n.

The total number of nodes for d orbital = l + (n - l) - 1
The total number of nodes for d orbital = n - 1

The total number of nodes for a orbital = n - 1
The total number of nodes for 3d - orbital = 3 - 1
                                                            = 2

                                     For d- orbital, l =2
                 Number of angular nodes = l = 2
                 Number of radial nodes = (n - l) - 1
                                                   = (3 - 2) - 1 = 0

All the five d orbitals belonging to a principal shell have the same energies. The size and energies increase with increase in the principal quantum number.

The energy of an electron exclusively depends on principal quantum number and not on Azimuthal quantum number.

Ex: The energy of an electron present in 3s, 3p or 3d remains the same irrespective of different values of Azimuthal quantum number.

Unlike the single-electron species, the energy of an electron in a multi-electron atom depends on Azimuthal quantum number also in addition to principal quantum number.

In a multi electron atom, the different energies of different orbitals of a given principal shell is attributed to the inter-electronic repulsions among the electrons. But in hydrogen atom it is due to the presence of only one electron the only electrical interaction present is the Electrostatic forces of attraction between the nucleus and the electron.

The complete attractive interactions of the positive charge are not experienced by the outermost electrons as the electrons in the inner shells tend to shield the electrons in the outer shells from positive attraction of nucleus. Thus the net positive charge experienced by the outermost electrons from the nucleus is called Effective nuclear charge and the shielding of outermost electrons from the attractive forces of nucleus by the inner shell electrons is called shielding effect or screening effect.

The attractive and repulsive interactions in a multi electron atom depend upon the shape of the orbital and shell.

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