Point out the followings: (a) How many energy subshells are possible in \(n=3\) level. (b) How many orbitals of all kinds are possible in \(n=3\) level.

In quantum chemistry, a principal concept that often bewilders students is that of 'energy subshells'. The term subshell refers to a division within an electron shell (designated by the principal quantum number 'n'), which is an energy level of an atom. An atomic shell can contain one or more subshells, and each subshell can accommodate a different number of electrons.

To visualize this, imagine each shell as a house with different rooms (subshells) where electrons 'live'. The principal quantum number tells us the 'address' of the house, in this case, the 'n=3' level. According to the rules of quantum mechanics, the 'n=3' shell has three rooms—these are the energy subshells, which are named 3s, 3p, and 3d. Each room has a specific capacity for electrons, but what determines this capacity? This leads us directly to another concept: the azimuthal quantum number.

When delving deeper into the structure of atoms, you will encounter the term 'atomic orbitals'. These are essentially the rooms within the subshells where electrons reside; they are described by a combination of three quantum numbers. Each orbital can hold up to two electrons, each with opposite spins. Picture an orbital as a region of space within an atom where there is a high probability of finding an electron.

For instance, within the 'n=3' energy level, we have the 3s orbital, three 3p orbitals, and five 3d orbitals, making it more of a mansion than a simple house! The concept of orbitals becomes tangible when we consider that each type (s, p, d, f) has a distinct shape. The s orbitals are spherical, p orbitals are dumbbell-shaped, and d orbitals have more complex cloverleaf shapes. There's an inherent beauty in how the seemingly chaotic world of quantum particles is organized into these orderly structures. Knowing the number of orbitals available within a given energy level enables us to understand electron configurations and predict chemical properties of elements.

The azimuthal quantum number, commonly denoted as 'l', plays a crucial role in characterizing subshells within an atom. This number can take on any integer value from 0 up to n-1 for a given principal quantum number n. Each value of l corresponds to a particular subshell (or room) where 0 is for s subshells, 1 for p, 2 for d, and so on. The azimuthal quantum number is akin to a label that tells us more about the shape and energy of each orbital within a subshell.

Let's apply this concept step by step to our original question involving the n=3 level. In this energy level, therefore, 'l' can be 0, 1, or 2. These values correspond to the 3s, 3p, and 3d subshells respectively. Each subshell type has a set number of orbitals, which we compute using the formula 2l + 1. Hence, for the s, p, and d subshells at the n=3 level, we get one, three, and five orbitals, respectively. By understanding the azimuthal quantum number, we gain insight into not just the 'address' (shell and subshell) but also the 'floor plan' (the types and numbers of orbitals) where electrons can be found.