# Atomic Structure

## Shapes of s, p and d orbitals

Boundary Surface Diagrams of constant probabilty density for different orbitals give a fairly good representation of the shapes of the orbitals. In this representation, a boundary surface is drawn in space for an orbital on which the value of probability density is constant. For a given orbital, only that boundary surface diargam of constant probability density is taken to be good representation of the shape of the orbital which encloses a region or volume in which the probability of finding the electron is very high, say, 90%.

1s and 2s orbitals are spherical in shape. In reality all the s-orbitals are spherically symmetrical. It means that the probability of finding the electron at a given distance is equal in all the directions. It is also observe that size of s orbital increases with increase in n. So, 4s > 3s > 2s > 1s.

Fig Ref: Energy Wave Theory

The shape of p-orbitals is similar to a dumbbell. Boundary surface diagrams of 2p orbitals show that each p orbital consist of two sections called lobes. These lobes are on either side of the plane that passes through the nucleus. The probability density function is zero on the plane where the two lobes touch each other. The size, shape and energy of the three orbitals are identical. But they differ in orientations of lobes. As the lobes may be considered to lie along x, y or z axis, they are represented by 2p_{x}, 2p_{y} and 2p_{z}.

The shape of d-orbitals is more complicated than that of p-orbitals. The four d-orbitals look like two dumbbells perpendicular to each other and intersecting through their mid-points. The fifth d-orbital looks like a doughnut surrounding a dumbbell.

The five d-orbitals are designated as d_{xy}, d_{yz}, d_{xz}, d_{x2y2} and d_{z2}. The shapes of the first four d-orbitals are similar to each other but shape of the fifth one is different.

## Filling of Orbitals in Atom

### Aufbau Principle

The word ‘aufbau’ in German means ‘building up’. According to aufbau principle: In the ground state of atom, orbitals are filled in order of their increasing energies.

Energy of a given orbital depends upon effective nuclear charge and different type of orbitals are affected to different extent. Thus, there is no single ordering of energies of orbitals which will be universally correct for all atoms. However, following order of energies of the orbitals is extremely useful:

*1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 4f, 5d, 6p, 7s...*

### Pauli Exclusion Principle

According to this principle: No two electrons in an atom can have the same set of four quantum numbers. Pauli exclusion principle can also be stated as : “Only two electrons may exist in the same orbital and these electrons must have opposite spin.”

This means that the two electrons can have the same value of three quantum numbers n, l and m_{l}, but must have the opposite spin quantum number. The maximum number of electrons in the shell with principal quantum number n is equal to 2n^{2}.

### Hund’s Rule of Maximum Multiplicity

This rule deals with the filling of electrons into the same subshell. According to Hund’s rule: pairing of electrons in the orbitals belonging to the same subshell (p, d or f) does not take place until each orbital belonging to that subshell has got one electron each i.e., it is singly occupied.

Since there are three p, five d and seven f orbitals, therefore, the pairing of electrons will start in the p, d and f orbitals with the entry of 4th, 6th and 8th electron, respectively. It has been observed that half filled and fully filled degenerate set of orbitals acquire extra stability due to their symmetry.

Completely filled and half filled orbitals are more stable. So, in some cases electrons may shift from lower energy orbital to higher energy orbital to ensure stability.

Cr (24) and Cu ( 29) show examples of such electronic configuration.

Cr (24) *1s ^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{1} 3d^{5}*

Above electronic configuration of Cr is stable because 3d orbital is half filled (5 electrons). So, it is *4s ^{1} 3d^{5 }* instead of

*4s*

^{2}3d^{4}Cu (29) *1s ^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{1} 3d^{10}*

In this case, the configuration is *4s ^{1} 3d^{10}* instead of

*4s*

^{2}3d^{9}