# How Many Orbitals Are There in the Third Shell (n=3)?

In chemistry, an orbital is a mathematical function that describes the probability of finding an electron in a specific region around an atom’s nucleus. The number of orbitals in each shell is determined by the principal quantum number, n. The third shell (n=3) can hold a maximum of 18 electrons, but how many orbitals does it have? In this article, we will explore the answer to this question and delve deeper into the world of atomic orbitals.

## Understanding Electron Shells and Orbitals

Before we dive into the specifics of the third shell, let’s take a quick look at electron shells and orbitals in general. The electrons in an atom are arranged in different energy levels or shells, with the closest shell to the nucleus being the first. The number of electrons in each shell corresponds to the shell’s capacity, which is determined by the formula 2n^2, where n is the principal quantum number.

Each electron in an atom occupies a specific orbital, which is characterized by a set of four quantum numbers – the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (m), and the spin quantum number (s). These numbers determine the size, shape, and orientation of the orbital.

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## The Third Shell (n=3)

The third shell, also known as the M shell, has a principal quantum number of 3. According to the formula 2n^2, the third shell can hold a maximum of 18 electrons. But how many orbitals are there in the third shell?

To determine the number of orbitals in the third shell, we need to consider the azimuthal quantum number (l), which defines the shape of the orbital. The possible values of l for the third shell are 0, 1, and 2. For l=0, the orbital is an s orbital, which is spherical in shape. For l=1, the orbital is a p orbital, which has a dumbbell shape with two lobes along the x, y, or z axes. For l=2, the orbital is a d orbital, which has a more complex shape with four lobes.

The number of orbitals in each subshell is determined by the formula 2l+1. Therefore, the third shell has:

• 1 s orbital (l=0)
• 3 p orbitals (l=1)
• 5 d orbitals (l=2)

Adding up the number of orbitals in each subshell gives us a total of 9 orbitals in the third shell.

## Conclusion

In conclusion, the third shell (n=3) has a total of 9 orbitals – 1 s orbital, 3 p orbitals, and 5 d orbitals. Understanding the number and types of orbitals in each shell is crucial to understanding the behavior and properties of atoms and molecules.

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