Lessons 8 & 9: Periodic Trends & Atomic Radii

Properties 1 & 2 – Atomic and ionic radius

Definition: the distance between the nucleus of an atom or an ion and the outermost electrons of the atom or ion

Atomic radii are determined by using two atoms of the same element bonded together and measuring the distance between the two nuclei, and then dividing by two to find the atomic radius. The elements where this is easiest to find are diatomic atoms, or atoms of the same element that often bond to themselves.

For example:

To find the atomic radius of H, we can measure the distance between the two nuclei in an H₂ molecule and divide it by two. Based on common measurements, we have found that the length of the bond between the two H atoms is about 74 pm. Dividing this by 2 gives an atomic radius for H of 37 pm.

Note: The reason we can find the distance between two nuclei but not between the center of the nucleus and the edge of the atom is because we don’t know the definite outer boundary of an atom.

Property 3 – Ionization energy

Definition: the amount of energy that is required to remove an electron off a given atom.

The different amounts of energy to remove each electron are categorized in the order in which each one would be removed. Each amount of energy is labeled as first ionization energy, second ionization energy, etc. To know from which subshells they are removed, we use the same order of electron subshells as in finding which are removed to form cations, as shown in Lesson 7.

The order followed in Lesson 7 for which electrons are removed is the same order in which we’d label first, second, etc ionization energies.

Property 4 – Electronegativity

Definition: the relative strength of an atom to pull electrons toward itself when bonded to another atom, or the power of an atom to attract electrons to itself when bonded to another atom.

For example:

In a water molecule, O is bonded covalently to two H atoms. We know that covalent bonds are where electrons are shared by atoms, which bonds them together. However, O has a higher electronegativity than H, so the electrons in the bonds are pulled closer to the O atom than the H atoms. This makes the O atoms in water molecules slightly negative and the H atoms slightly positive, which is the reason why we call water a polar molecule.

Property 5 – Electron affinity

Definition: the amount of energy released when a stray electron is taken or “captured” by a given atom.

This is a similar concept to ionization energy, and follows a similar labeling system, but is for when electrons are added to an atom, not taken away.

There are four factors that affect the previously shown atomic properties that we will focus on.

Factor 1 – Nuclear charge

Definition: the amount of protons in an atom’s nucleus.

This value, represented by the variable Z, is equal to the atomic number of an atom.

Factor 2 – Effective nuclear charge

Definition: the attractive force that the nucleus exerts on outermost electrons.

This value, represented by the variable Z*, represents how strongly the electrons in the outermost layer are being pulled toward the nucleus of an atom. For these purposes, we can calculate Z* by subtracting how many electrons there are in all layers besides the outer layer (the total of all inner electrons) from the Z value.

For example:

To find the Z* value of H, we know that the Z value is 1 and there are no inner electrons. This gives us Z* = 1 – 0, or Z* = 1.

To find the Z* value of N, we know that the Z value is 7 and the amount of inner electrons is 5. This gives us Z* = 7 – 2, or Z* = 5.

Factor 3 – Shielding

Definition: the amount of inner shells of electrons around atom that “protect” the outermost electrons from the pull of the nucleus.

Shielding is done by all the electron shells except for the outermost shell.

Factor 4 – Energy level of outermost electrons

Definition: the energy of the highest energy subshell within the highest energy shell.

To find which subshell this is referring to, find the highest shell first, then find the highest subshell that is in that shell.

Final note on atomic radii:

Atomic radii are primarily determined by the Z* value and the highest (outermost) electron shell. Elements within the same group on the periodic table have the same Z* value. The Z* value increases by one for each element moving to the right within the same period on the periodic table. The atomic radius increases for each element moving down each group, since there is a new electron shell in each period. As the Z* value increases going to the right, the atomic radius becomes smaller. This is because the Z* value represents how strongly the nucleus is pulling on the outermost electrons, becoming stronger moving right in each period on the periodic table. This pulls the electrons closer to the center, shrinking the radius of the atom overall. This is mostly consistent, with a few exceptions such as the radius staying mostly constant in the d block on the periodic table.