Shapes of Atomic Orbitals: Orbitals Chemistry, Shapes of s, p, d, f

The atomic orbitals are of different shapes, where the s orbital has a spherical shape, the p orbital has a dumbbell shape, and four of the five d orbitals have a cloverleaf shape. The fifth d orbital has a shape of an elongated dumbbell with a doughnut around its middle. The orbitals in an atom are organized into different layers or electron shells. Atomic orbitals describe the most likely location of the electrons that will be found around the nucleus of an atom; every unique orbital can comprise only up to two electrons. Let’s have a closer look at the topic with some important questions.

Key takeaways: Orbitals chemistry, shapes of atomic orbitals, the s orbitals, p orbitals, the d orbitals, the f orbitals, orbital wave function.

NCERT Solutions of:

Class 11 Chemistry Chapter 2 Structure of Atom​

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What are Atomic Orbitals?

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The 3-dimensional space around the nucleus of an atom where the possibility of finding an electron is the highest is called an atomic orbital.

In an atom, there exist many orbitals. These orbitals, further, exist in various shapes. A small sized orbital means there is a higher probability of finding an electron near the nucleus.

Read More: Cannizzaro Reaction Mechanism

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Orbital Wave Function

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The varied shapes and orientation of atomic orbitals state that there is either no or a greater probability of finding an electron near the nucleus along some directions. According to the quantum atomic model, an atom can have various possible orbitals which can be categorized on the basis of their shape, size or orientation. The orbital wave function or \(\Phi \) is a mathematical function that is used to denote the coordinates of an electron. The square of \(\Phi \) indicates the probability of finding an electron in the orbital. \(\Phi \) helps in drawing out the boundary surface diagrams. The shape of the atomic orbitals can be understood by boundary surface diagrams of the constant probability density for different orbitals. All the information of an electron in an atom is stored in its orbital wave function i.e. \(\Phi \).

The probability of finding an electron in an atom is proportional directly to \(\Phi ^2\) which is called as probability density which is, further, always positive. Each atomic orbital is denoted by a specific number and a specific letter, called quantum numbers. Each orbital is denoted by three quantum numbers, n, l and m. The number against an orbital is indicated by the energy level of the electron in that orbital.

The energy level closest to the nucleus is 1; the next one is 2 and so on. The symbols of the orbital shapes i.e. s, p, d and f come from the words meaning sharp, diffuse, principal and fundamental respectively. Of the four orbitals, the s and p orbitals are considered significant because they are the commonly used orbitals in organic and biological chemistry.

Read More: Dalton’s atomic theory

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Nodes

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They are the region where the probability of finding an electron would be zero. The nodal plane is the plane which passes through the nucleus where the probability of finding an electron is zero.

In any orbital, the number of nodal planes is equal to I i.e. the Azimuthal quantum number.

The two types of nodes are: radial and angular nodes. The radial nodes are the spheres at fixed radius that occur as the principal quantum number increases while angular nodes are flat at fixed angles.

The total number of nodes of an orbital is the sum of the radial and angular nodes. It is represented in terms of n and I quantum number, N = n - I - 1

Read More: Franck Hertz Experiment

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The s Orbitals

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1. The shape of the s orbital is spherical with the nucleus in the centre.

2. The boundary surface diagram for the s shaped orbital is similar to a sphere with a nucleus at its centre. In two dimensions, it can be seen as a circle.
3. Therefore, s orbitals can be said to be spherically symmetrical.
4. Due to their symmetry, they have the probability of finding an electron at equal distances from the nucleus.
5. The size of the s orbital is found to increase with increase in the value of principal quantum number (n). Hence, 4s > 3s > 2s > 1s.

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The p Orbitals

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1. All p orbitals contain two sections called lobes that lie on either side of the plane which passes through the nucleus of the atom.
2. The three p orbitals are identical in terms of shape, size and energy. However, they differ in their orientation of lobes.
3. Since the lobes lie along one out of the three axes, namely, x, y and z, the three orbitals are designated as 2px, 2py and 2pz. It can thus be said that there are 3 p orbitals with mutually perpendicular axes.
4. As in s orbitals, the energy and size of p orbitals increases with an increase in the quantum number i.e. 4p > 3p >2p.

Read More: Charge to Mass Ratio of Electron

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The d Orbitals

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1. The magnetic orbital quantum number for d orbitals is denoted as (-2, -1, 0, 1, 2). Thus, there exist five d orbitals.
2. The d orbitals are given the designations d_xy, d_yz, d_xz, d_x²-_y² and d_z².
3. The shapes of the first four d orbitals are similar to one another while being different from the dz2 orbital.
4. The energy of all five d orbitals is the same.

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The f Orbitals

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1. The f orbitals have corresponding magnetic quantum numbers m1 (-3, -2, -1, 0, 1, 2 3).
2. They have the secondary quantum number I = 3.
3. They are buried deeply beneath the valence shell for the elements that are even beyond cerium since; they are not occupied in the ground state until the element cerium.
4. The f orbitals are given the designations and f_z³.
5. Each f orbital has a multi-lobed and complex shape with several nodal points.
6. The 4f_y³- _3x²_y orbital corresponds to l = 3, ml = -3, and n = 4

The 4f_xyz orbital corresponds to l = 3, ml = -2, and n = 4.

The 4f_5yz²- yr² orbital corresponds to l = 3, ml = -1, and n = 4.

The 4f_5z³- _3zr² orbital corresponds to l = 3, ml = 0, and n = 4.

The 4f_5xz²- _xr² orbital corresponds to l = 3, ml = +1, and n = 4.

The 4f_zx³- _xy² orbital corresponds to l = 3, ml = +2, and n = 4.

The 4f_x³- _3xy² orbital corresponds to l = 3, ml = +3, and n = 4.

7. The f orbitals have three nodal planes and complex shapes with the atomic nucleus at the centre.

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Points to Remember

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1. Orbits and orbitals are two different concepts: Orbit is a well-defined circular path in the atom in which the electrons move around the nucleus whereas orbitals are the three-dimensional space around the nucleus of an atom in which the probability of finding an electron is the highest.
2. The nodal plane is the plane where the probability of finding an electron is Zero.
3. Out of all the orbitals, only the s orbitals are non-directional.
4. The orbital 1s holds the highest energy.
5. Difference between a shell and an orbital: A shell in an atom is a set of sub-shells of the same quantum number theory i.e. n, while orbitals consist of two electrons each.

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