Question

(a) What is the numbering system used to label shells? (b) What is the lettering system used to label subshells? (c) How many subshells are there in a given shell?

Short answer

(a) Shells are labeled using principal quantum number (n), with positive integers (n=1, 2, 3, etc.) indicating increasing energy levels. (b) Subshells are labeled using azimuthal quantum number (l) and corresponding letters (0='s', 1='p', 2='d', 3='f'). (c) There are n subshells in a given shell, with n being the shell's principal quantum number.

Step-by-step solution

(a) Numbering System for Shells

The shells in an atom are labeled using the principal quantum number (n), which is a positive integer. The lowest energy level, closest to the nucleus, is labeled as the first shell with n=1. As we move away from the nucleus, the energy levels increase, and the shells are labeled using successive integers (n=2, n=3, n=4, etc.).

(b) Lettering System for Subshells

Subshells within a shell are labeled using the azimuthal quantum number (l), which is an integer ranging from 0 to n-1, where n is the shell number. Each value of l corresponds to a specific letter designation for the subshell: 0 is represented by the letter 's', 1 by 'p', 2 by 'd', and 3 by 'f'. This sequence continues with the English alphabets, but in practice, only 's', 'p', 'd', and 'f' orbitals are usually encountered.

(c) Number of Subshells in a Given Shell

The number of subshells in a given shell depends on the shell's principal quantum number (n). As mentioned before, the azimuthal quantum number (l) ranges from 0 to n-1. Therefore, there are n different values of l for each shell, which means there are n subshells in a given shell. For example, if n=3, then there are 3 subshells (l=0, 1, 2 or 's', 'p', 'd' subshells) in that shell.

Key concepts

Principal Quantum Number

The principal quantum number, symbolized as 'n', is akin to the address of an electron within an atom. Think of it as the floor number in a high-rise building, where higher floors represent electrons that are further from the atom's nucleus. The value of 'n' starts at 1 (the ground floor) for the electrons closest to the nucleus and increases in whole numbers as the electrons are found in layers further out.

As 'n' increases, so does the energy level of an electron, allowing us to understand why certain electrons have more energy than others. Electrons in higher principal quantum levels (higher 'floors') are less tightly bound to the nucleus and, therefore, can have more complex movements and interactions. In chemistry, these distinctions are crucial for understanding how elements react and form compounds.

Azimuthal Quantum Number

Moving on to the azimuthal quantum number, represented by 'l', we dive into a subdivision of the principal quantum number. Imagine each 'floor' of our electron 'building' has different rooms; the 'l' value tells us the shape of these rooms, commonly called 'subshells'.

Each subshell is denoted by a specific letter that corresponds to its value: 's' (l=0), 'p' (l=1), 'd' (l=2), and 'f' (l=3). The s-subshell is spherical, p is dumbbell-shaped, and d and f are more complex. These shapes indicate the probability of finding an electron in a certain area around the nucleus, and thus, they are critical for visualizing how electrons inhabit atomic space and how they can engage with other electrons during chemical reactions.

Energy Levels in Atoms

Discussing energy levels in atoms helps us understand why electrons reside at certain distances from the nucleus. Each principal quantum number (n) defines a main energy level, and within these levels are sublevels, determined by the azimuthal quantum number (l).

Just as with the floors of a building, higher levels require more energy to reach. Electrons naturally occupy the lowest possible energy levels, a concept known as the Aufbau principle. However, through the absorption of energy, electrons can 'jump' to a higher level, this is the core of many phenomena such as spectral lines and the process of photosynthesis.

Atomic Orbitals

The term 'atomic orbitals' is the detailed description of where electrons are most likely to be found within an atom. Unlike planets orbiting the sun, electrons exhibit a wave-like behavior, making their exact position uncertain. Therefore, orbitals are visual models that provide a statistical map of an electron's location.

Each orbital type (s, p, d, f) has a distinct shape and orientation in space, which allows electrons to be distributed throughout an atom in a way that minimizes repulsion between them. Understanding orbitals is fundamental to grasping how chemical bonds form, predict molecular shapes, and how the electrons contribute to the chemical properties of elements.