Learning Objectives Describe how electrons are grouped within atoms into shells, subshells, and orbitals using quantum numbers. You now know that the periodic table is arranged in groups and periods (columns and rows) based on chemical and physical properties of the different elements. The first element, hydrogen ( Z =1) has one proton and one electron and as you move right across the rows, each subsequent element has one additional proton and electron. You may have asked yourself, why are periodic trends observed across the rows and down the groups? Or, why do the rows have different numbers of elements, giving the table a unique shape? These questions can be answered by learning more about the electrons in atoms. Although we have discussed the general arrangement of subatomic particles in atoms, we have said little about how electrons occupy the space around the nucleus. Do they move around the nucleus at random, or do they exist in some ordered arrangement? In 1913, the Danish scientist Niels Bohr suggested that the electron in a hydrogen atom could not have any random energy, having only certain fixed values of energy that were indexed by the number n (now called a quantum number ). Bohr suggested that the energy of the electron in hydrogen was quantized because it was in a specific orbit; much like the steps on a staircase does not have half or quarter stairs or the keys on a piano don't have notes in between, there are no energy levels in between each orbit. Figure \(\PageIndex{1}\) shows a model of the hydrogen atom based on Bohr's ideas. Bohr's ideas were useful, but were applicable only to the hydrogen atom. However, later researchers generalized Bohr's ideas into a new theory called quantum mechanics , which explains the behavior of electrons as if they were acting as a wave, not as particles. Quantum mechanics predicts two major things: quantized energies for electrons of all atoms (not just hydrogen) and an organization of electrons within atoms. Electrons are no longer thought of as being randomly distributed around a nucleus or restricted to certain orbits (in that regard, Bohr was wrong). Instead, electrons are collected into groups ( shells ) and subgroups ( subshells ) that explain much about the chemical behavior of the atom. In the quantum-mechanical model of an atom, which is the modern and currently accepted model, the location of electrons in the atom are described by four quantum numbers , not just the one predicted by Bohr. Much like your home address can be used to locate you in a specific state, city, street, and house number, the first three quantum numbers identify approximately where electrons are in an atom. The fourth quantum number describes the electron and whether it is spin up or down (clockwise or counterclockwise). The theory and mathematics behind these four quantum numbers are well beyond the scope of this textbook, however, it is useful to learn some of the basics in order to understand how atoms behave and interact with (react) with other atoms. Electron Arrangements: Shells, Subshells, and Orbitals Electrons are organized according to their energies into sets called shells (labeled by the principle quantum number, n ). Generally the higher the energy of a shell, the farther it is (on average) from the nucleus. Shells do not have specific, fixed distances from the nucleus, but an electron in a higher-energy shell will spend more time farther from the nucleus than does an electron in a lower-energy shell. Shells are further divided into subsets of electrons called subshells , labeled by type as s , p , d , or f . The first shell has only one subshell, s . The second shell has two subshells, s and p; the third shell has three subshells, s , p , and d, and the fourth shell has four subshells, s , p , d , and f . Within each subshell, electrons are arranged into different numbers of orbitals , an s subshell is made up of one s orbital, a p subshell has two p orbitals, a d subshell, five d orbitals, and an f subshell, seven f orbitals. Each orbital has a different shape and orientation around the nucleus (Figure \(\PageIndex{1}\), however, rather than representing an orbit, as the name suggests, orbitals define a boundary for the region of space where a given electron is most likely to be found. Lastly, a single orbital can hold up to two electrons each with a different spin . It is important to note that according to quantum theory, there are specific allowed combinations of quantum numbers and others that are not allowed. For example, shell two can only have two subshells, s with one orbital and p with 3 orbitals, therefore, this shell can hold a maximum of eight electrons (four orbitals times two electrons each). It takes practice to learn the allowed combinations as shown in Table \(\PageIndex{1}\) but it is helpful to visualize the atom as a sphere with the nucleus in the center. Close to the nucleus, there is a smaller amount of space for electrons – a smaller shell. As the number of electrons increases, the shells that hold the electrons get larger and thus further away from the nucleus. Shell (n) Number of Subshells Names of Subshells Number of Orbitals (per Subshell) Number of Electrons (per Subshell) Total Electrons (per Shell) 1 1 1s 1 2 2 2 2 2s and 2p 1, 3 2, 6 8 3 3 3s, 3p, and 3d 1, 3, 5 2, 6, 10 18 4 4 4s, 4p, 4d, and 4f 1, 3, 5, 7 2, 6, 10, 14 32 All of this information about the shell, subshell, and orbital is put together to make up the "address" for an electron and all of the addresses for all the electrons in an atom make up the electron configuration , which is described more later.