In lower classes, we were taught about the solar system model of an atom (Bohr’s Atomic Model). It made us think that the electrons revolved around the nucleus in elliptical orbits. But this is not the case. In this topic, we will learn about the Shapes of Atomic Orbitals.

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## Shapes of Atomic Orbitals

In an atom, there are a large number of orbitals. There are various shapes of atomic orbitals. An orbital which is of small size states that there is more chance of finding the electron near the nucleus. The shapes of atomic orbitals and the orientation define that there is no probability of finding the electron along some certain directions than among others.

In other words, orbitals are the regions of space in which electrons are usually to be found. Each of the orbitals is denoted by a number and a letter. Herein, the number is denoted by the level of energy of the electron in the orbital.

1 refers to the energy level that is closest to the nucleus, however, 2 refers to the next level of energy further out. The symbols s, p, d, f originally comes from the words meaning sharp, principal, diffuse and fundamental respectively. This has been used to ascertain the spectral lines in the atomic spectra of different atoms.

The total permitted values of m for a given value of I to give the number of orbitals of one type within a subshell. For example – there is one orbital of s – a type of the value of I is 0, 3 p – orbitals of the value of I is one, 5 d – orbitals if the value of I is 2 and so on.

## Determination of Shapes of Atomic Orbitals

### S – Orbitals

For the s orbital, the boundary surface diagram looks like a sphere having the nucleus as its centre which in 2 dimensions can be seen as a circle. The s – orbitals are spherically symmetric having the probability of finding the electron at a given distance equal in all the directions. With the increase in the value of a principal quantum number, say n, the size of the s orbital will also increase.

### P – Orbitals

Each p orbitals comprises of two sections referred to as lobes that lie on either side of the plane passing through the nucleus. All the three p orbitals vary in the way of the orientation of the lobes. However, they are very identical in terms of the size, shape, and energy. These lobes are placed along one of the x, y, z-axis and are given description 2px, 2py, and 2pz.

Therefore, we can say that there are about 3 p orbitals whose axes are mutually perpendicular. Just like the s – orbitals, with an increase in size and energy of p orbitals quantum number ( 4p > 3p > 2p ), the size and energy of p orbitals also increase.

### D – Orbitals

Magnetic orbital quantum number for d orbitals is given as ( -2, -1, 0, 1, 2 ). For which we can say that there are 5 d – orbitals which are designated as d_{xy}, d_{yz}, d_{zx}, d\( _{x^2 – y^2}\)^{ }and d\( _{z^2}\). Out of these 5 d orbitals, the shapes of the first 4 d – orbitals are similar to each other which are comparatively different from the dz2 orbital whereas the energy of all 5 d – orbitals is same.

## Solved Examples for You

Question: Which of the following d orbitals has a diagonal nodal plane?

- d
_{xy} - d
_{yz} - d\( _{x^2 – y^2}\)
- d
_{zx}

Solution: Option C. d\( _{x^2 – y^2}\)

Question: The electron density of 3d_{xy} orbital in YZ plane is:

- 50%
- 95%
- 33.33%
- 0%

Solution: Option D) 0%. YZ plane is a nodal plane for d_{xy} orbital. The electron density is only in XY plane.

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