# Why do atoms tend to have 8 valence electrons?

These responses can be grouped together. One can be taken as an independent.

The Schrodinger Equation refers to electrons as a type wave. This wave-like behavior explains why electrons can form standing waves in a medium that has boundaries.

Understanding standing waves on strings can help you to see how quantum numbers are formed. Only certain wavelengths can fit along strings with their ends fixed, and these can be numbered. The longest wavelength is n=1, and the second-largest wavelength is n=2, and so on.

The electrons create spherical waveforms around a nucleus. It is difficult to visualize spherical waves, so this may help you get an idea.

Their radial profile is given by the quantum number n. Two other quantum numbers, the l and the m, give their profiles in longitude and latitude. These waves can be viewed in the following:

By Inigo.quilez (Own work) CC BY-SA 3.0

People refer to “s” orbitals as ones with a uniform latitude/longitude profile. This is the blue sphere at top of the figure. The three images that have two lobes in row 2 are called “p” orbitals. Quantum numbers for “s” orbitals are n=1, 2, 3, and l=0. Quantum numbers for “p” orbitals are n=2,3,4…, and l=1. Three versions of the “p” orbital exist: m=-1; m=0… and l=1. These give rise to lobes that are oriented along three different axes.

The Pauli Exclusion Principle can be considered an independent issue. Chemistry would be boring if electrons were not fermions but bosons. At room temperature, the majority of electrons would fall to the lowest energy state. This would mean that most would be in the boring state n=1, and l=0. All chemical elements would exhibit the same behavior. The Pauli Exclusion Principle states that electrons are fermions and therefore cannot have the same quantum numbers. The n=1 and l=0 states are filled by helium. We must fill up the n=2, L=0 states for lithium and the n=2, L=1 states for boron.

From where did the number 8 come? In the above picture, you can see there is one s orbital and three p orbitals. There are two possible values of elecron spin. This gives you a fourth quantum number, m_s=-1/2 and m_s=+1/2. Each “s-orbital”, can hold two electrons, and each “p-orbital”, can hold six. 2 + 6 = 8.

Pauli Exclusion states that every electron must possess a unique set (n,l, m_s), The lowest energy state for hydrogen is (1.0,0.+1/2). However, m_s could also be +1/2 or 1/2, as the energies are identical. Two electrons make up the lowest energy state for helium. One has (1,0.0,-1/2), and one has (1,0.0,+1/2). Lithium has the lowest energy states (1,0.0,+1/2), (1.0.0,-1/2), and (2,0.0,+1/2). Beryllium has (1,0.0.+1/2), (1.0.0.-1/2), (2.0.0.-1/2), and (2.0.0.+1/2). Boron is (1.0.0.+1/2), (1.0.0.-1/2), (2.0.0.-1/2), (2.0.0.-1/2), and (2.0.0.+1/2).

You can also find orbitals with larger l values (dorbitals). The 5 states are shown in the third row of the image. This is why the transition metal block in the periodic table has 10 elements (count them from zinc to scandium). What are the elements in the “lanthanide bloc”?