8.4 The exclusion principle and the periodic table

So far, we have studied only hydrogen, the simplest chemical element. We have found that an electron in the hydrogen atom can be completely specified by five quantum numbers:

To construct the ground state of a neutral multi-electron atom, imagine starting with a nucleus of charge Ze (that is, a nucleus of atomic number Z ) and then adding Z electrons one by one. Assume that each electron moves in a spherically symmetrical electric field produced by the nucleus and all other electrons of the atom. The assumption is valid because the electrons are distributed randomly around the nucleus and produce an average electric field (and potential) that is spherically symmetrical. The electric potential U ( r ) for each electron does not follow the simple $\mathrm{-1}\text{/}r$ form because of interactions between electrons, but it turns out that we can still label each individual electron state by quantum numbers, $(n,l,m,s,m_s)$ . (The spin quantum number s is the same for all electrons, so it will not be used in this section.)

The structure and chemical properties of atoms are explained in part by Pauli’s exclusion principle    : No two electrons in an atom can have the same values for all four quantum numbers $(n,l,m,m_s).$ This principle is related to two properties of electrons: All electrons are identical (“when you’ve seen one electron, you’ve seen them all”) and they have half-integral spin $(s=1\text{/}2).$ Sample sets of quantum numbers for the electrons in an atom are given in [link] . Consistent with Pauli’s exclusion principle, no two rows of the table have the exact same set of quantum numbers.

Electrons with the same principal quantum number n are said to be in the same shell , and those that have the same value of l are said to occupy the same subshell . An electron in the $n=1$ state of a hydrogen atom is denoted 1 s , where the first digit indicates the shell $(n=1)$ and the letter indicates the subshell $(s,p,d,f\text{…}\text{correspond to}l=0,1,2,3\text{…}).$ Two electrons in the $n=1$ state are denoted as $1s^2,$ where the superscript indicates the number of electrons. An electron in the $n=2$ state with $l=1$ is denoted 2 p . The combination of two electrons in the $n=2$ and $l=0$ state, and three electrons in the $n=2$ and $l=1$ state is written as $2s^{2}2p^3,$ and so on. This representation of the electron state is called the electron configuration    of the atom. The electron configurations for several atoms are given in [link] . Electrons in the outer shell of an atom are called valence electron     s . Chemical bonding between atoms in a molecule are explained by the transfer and sharing of valence electrons.