Chemistry 101: Atomic Theory and Structure

The Bohr Theory states:

• Electrons can only exist in fixed orbits or energy levels.

• These energy levels are at specific distances from the nucleus.

• Any energy emitted/absorbed from/by an atom will be the result of an electron jumping from one energy level to another.

The Bohr Model states that the hydrogen electron orbits the nucleus.

Note: all models assume that electrons orbit the nucleus, but Bohr’s model is unique in that in most chemistry courses and on the AP Chemistry exam, the Bohr model is usually restricted to the hydrogen atom only.

In a spherical probability cloud around the nucleus, called the 1s orbital.

Note: the quantum mechanical model is the one used in most chemistry courses and on the AP Chem exam.

The atomic electron is in the ground state.

The ground state is the lowest possible energy orbital that any atomic electron may occupy.

The hydrogen electron moves into an excited state.

Ex: a ground-state electron in hydrogen is in the 1s state. If it absorbs the right amount of energy, it can jump into the 3p state, which is excited (higher) in energy than the ground state.

The electron must absorb energy, typically in the form of a photon, to go from the ground state to an excited state.

Energy flows out of the atom when an electron drops to the ground state.

Since the ground state is lower in energy than the excited state, the change from excited to ground is always accompanied by a release of energy from the atom.

The absorption spectrum is the unique set of wavelengths of light absorbed by a specific substance or medium.

The absorption spectrum is typically displayed as a set of dark lines (or missing lines) in the spectrum, representing the absorbed wavelengths. This is the third bar in the image.

The emission spectrum is the unique spectrum of bright lines or bands of light emitted by a particular substance when it is electronically excited.

This is the second bar in the image.

The absorption and emission spectral lines will overlap with one another perfectly.

Both absorption and emission energy values are dependent on electrons moving between energy levels. Jumping to a higher level (dark absorption line) should be in the exact same position as jumping to a lower level (bright emission line) since it’s the exact same amount of energy absorbed and emitted, respectively.

n is the principal quantum number, and is commonly referred to as the shell the electron is in.

n can have any whole number value greater than or equal to 1.

As n increases, energy increases.

Remember: assume that the quantum number l stays constant unless told otherwise.

1. l is the angular momentum (or azimuthal) number.

2. It represents an electron’s subshell.

If l = 0, the electron is in an s subshell.
If l = 1, the electron is in a p subshell.
If l = 2, the electron is in a d subshell.
If l = 3, the electron is in a f subshell.

l can take any integer value from 0 to n - 1, but most chemistry courses and the AP Chem exam will only explicitly test 0 to 3.

1. The letters s, p, d, f symbolize the subshells in which an electron can exist.

2. The value of the quantum number l determines the subshell. s, p, d, and f subshells correspond to l = 0, 1, 2, and 3, respectively.

1. m or ml is the magnetic quantum number.

2. It represents the orbital in which an electron exists.

m can hold any integer value between -l and +l, including 0.

Ex: for an electron whose l = 1 (p subshell), m can equal -1, 0, or 1. These values correspond to the px, py, and pz orbitals, respectively.

A p subshell has three orbitals: px, py, and pz.

Remember: l = 1 for any p subshell. ml can range from -l to l (in this case: -1, 0, or 1) in a p subshell. These values correspond to the x, y, and z orbitals.

1. s or ms is the spin quantum number.

2. It represents the spin direction of an electron.

s can have exactly one of two values, +1/2 and -1/2, corresponding to spin-up and spin-down. These two values are inherently equal in energy.

For any s electron, l = 0.

l can range from any value from 0 to n-1, and determines the subshell. By definition, if l = 0 for an electron, that electron exists in an s orbital.

Each orbital can hold up to 2 electrons.

Note: When one orbital hold two electrons simultaneously, one must be spin-up and the other spin-down.

A d subshell holds up to 10 electrons.

Each of the 5 orbitals can have 1 spin-up electron and 1 spin-down, for a total of 2(5)=10 total.

• 
  s = ‘spherical’

• p = ‘peanut’

• d = ‘donut’

There are 2n2 electrons in the filled shell.

Ex: For the n = 2 shell: 2(22) = 8

This shell has 4 orbitals: 2s, 2px, 2py, 2pz. Each of those can hold 2 electrons, for a total of 8 in the shell.

A shell will have n2 orbitals.

Ex: For the shell n = 2 there are 22 = 4 orbitals total. They are the 2s, 2px, 2py, and 2pz orbitals.

A subshell will have 2(l) + 1 orbitals.

Ex: For a d subshell, l = 2, so there are 2(2) + 1 = 5 orbitals total. They are the dxy, dxz, dyz, dx2-y2, and dz2 orbitals.

• An s subshell holds 1x2=2 electrons

• A p subshell holds 3x2=6 electrons

• A d subshell holds 5x2=10 electrons

• An f subshell holds 7x2=14 electrons

The subshell with the lowest total energy will fill first.

Total energy can be approximated as E=n+l, where n=principal quantum # and l=azimuthal quantum #.

Ex: For a 4s subshell, n = 4 and l = 0, so n+l = 4. So a 4s subshell will fill before a 3d subshell, which has n = 3, l = 2, and n+l = 5.

Note: in the case of a tie between two subshells with the same n+l value, the one with the lower n will fill first.

In order of increasing energy:

2s \< 4s \< 3d \< 6s \< 4f

The total order of all relevant subshells in the full Periodic Table is:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d

In order of increasing energy:

s \< p \< d \< f

These subshells differ in their value of l. For a given n, the higher the l, the higher the energy.

The spectroscopic notation denotes the three most important pieces of information about a subshell: its energy level (n), subshell (l), and the total number of electrons it contains.

So Chromium's 3d5 explains that there are 5 valence electrons, with n = 3 and l = 2.

The full electronic structure of Calcium is:
1s22s22p63s23p64s2

In condensed notation:
[Ar] 4s2

Since every up to 3p6 is completely filled, they are not chemically relevant - only valence electrons participate in chemical reactions. Therefore, they can all be abbreviated as the noble gas from the previous row, in this case Ar, which represents the element with fully-filled subshells up to 3p6.

The Aufbau Principle describes the order in which subshells are filled with electrons as atomic number increases. Aufbau is German for 'Building Up'.

Shells/subshells of lower energy get filled with electrons before higher energy shells/subshells.

Ex: The 1s subshell fills first, then 2s, then 2p, and so on.

Hund's Rules describe the order of adding electrons to an unfilled subshell.

Hund's Rules explain that when electrons are added to a subshell that has more than 1 orbital (p, d, or f), each orbital first receives a single electron, each spin-up, until each orbital in the subshell has one electron contained within it.

Only once the orbital is half full will spin-down electrons be added, one per orbital, until the subshell is completely filled.

The Pauli Exclusion Principle states that two electrons in the same orbital must be of different spins.

The result of this rule is that two electrons in the same atom will never have exactly the same 4 quantum numbers (n, l, ml, ms).

Fully-filled and half-filled subshells make atoms particularly stable.

In particular, atoms with p3, p6, d5, and d10 valence shell configurations are especially stable.

A classic question will ask about exceptions to typical stability trends, and the answer will be due to an atom having a half-filled subshell.

Phosphorus' valence shell configuration is 3p3, while sulfur's is 3p4.The p-block electrons around phosphorus will therefore be more stable, as the p subshell is half-filled with parallel-spin electrons, a particularly stable configuration.

Sulfur will be slightly less stable, as its p subshell contains one additional electron paired in an orbital with an anti-parallel spin electron.

The effective nuclear charge Zeff is the amount of attraction that an electron in the outermost subshell has towards the positively-charged nucleus.

This number can be calculated by calculating the positive charge of the nucleus and subtracting the total number of shielding electrons in the inner, fully-filled subshells.

The higher the Zeff, the more strongly the outer electrons in unfilled subshells are bound to the atom.

Zeff (Na) = +1.

Na has 11 total protons in the nucleus, and 10 total electrons in inner subshells (1s2,2s2, 2p6), so:

Zeff(Na) = +11 - 10 = +1

Zeff (S) = +6.

S has 16 total protons in the nucleus, and 10 total electrons in inner subshells (1s2,2s2, 2p6), so:

Zeff(S) = +16 - 10 = +6

Alkali metals make up the first column of the Periodic Table (Group IA).

1. All alkali metals have an s1 valence shell configuration.

2. Alkali metals are relatively electropositive, so will lose 1 valence electron and form a +1 oxidation state.

Alkaline earth metals make up the second column of the Periodic Table (Group IIA).

1. All alkaline earth metals have an s2 valence shell configuration.

2. They are relatively electropositive, so will lose 2 valence electrons and form a +2 oxidation state.

The halogens make up the fifth column of the p block (Group VIIA).

1. All halogens have an s2p5 valence shell configuration.

2. They are quite electronegative, so they will accept one additional valence electron to take on a -1 oxidation state.

The noble gases make up the sixth column of the p block (Group VIIIA).

1. All noble gases have an s2p6 valence shell configuration.

2. Trick question! Since they already have a completely filled octet, noble gases do not ionize, and they typically exist in the 0 oxidation state as free particles.

Exception: Kr and Xe, being below the 3rd row, can exceed their octet and make coordinate covalently bonded compounds such as XeF6.

The oxygen group is the group (column) below oxygen on the Periodic Table.

It includes elements such as S and Se that are chemically similar to oxygen.

The transition metals make up the entire d block.

Transition metals have high conductivity due to their unfilled d subshells.

d electrons, by their nature, are loosely bound to the atom. As such, elements with partially-filled d subshells can be thought of as nuclei floating in a sea of unattached electrons, prime conditions for electrical conductivity.

Representative elements are the most common elements in the solar system and the universe.

They are found in the s block and the p block of the Periodic Table.

By standard nomenclature, these are groups IA, IIA, IIIA, IVA, VA, VIA, VIIA, and VIIIA.

The elements of the first two columns have a valence s subshell.

Group IA has an s1 valence configuration, while IIA is s2.

Note: helium also has a valence s subshell, but is typically listed on the farthest column with the noble gases, as it is chemically more similar to them than the alkaline earth metals.

The elements of the last six columns have a valence p subshell.

Ex: Group IIIA has an s2p1 valence configuration, while VIIIA is s2p6.

Note: Although helium is typically listed on the farthest column with the noble gases in VIIIA, it actually has a valence s subshell.

Metals are generally:

• found in the lower-left areas of the periodic table.

• low in electronegativity, losing electron density when bonded to nonmetals.

• found in positive oxidation states when in compounds.

Metals generally are/have:

• good conductors of heat and electricity.

• malleable, ductile, lustrous, and dense solids at room temp.

• fairly high melting and boiling points.

Nonmetals are generally:

• found in the upper-right areas of the periodic table.

• high in electronegativity, gaining electron density when bonded to metals.

• found in negative oxidation states when in compounds.

Nonmetals are/have:

• poor conductors of heat and electricity.

• dull and brittle if they form solids at room temperature.

• significantly lower melting and boiling points than metals (carbon is the primary exception).

Oxygen has 6 valence electrons.

Oxygen is the 6th element in its row. Its valence shell configuration is 2s22p4, for a total of 6 valence electrons.

The energy required to remove one valence electron from an atom in the gas phase.

The generic ionization energy equation is: X(g) ⇒ X+(g) + e-

Ionization energy increases from left to right across a row of the Periodic Table.

Other notes about ionization energy:

Atoms with fully-filled subshell will have high ionization energies.
Atoms with half-filled subshells will have higher ionization energies than their neighbors.
The alkali and alkaline earth metals have very low ionization energies.

Cl

Remember: ionization energy decreases going down a column. Br is below Cl in the halogen column.

Ionization energy decreases heading down a column of the Periodic Table.

The further down a column an element lies, the easier to remove. These atoms have higher n values for their valence electrons. Higher n electrons sit further from the atomic nucleus, and are therefore less strongly bound to the nucleus.

P

Remember: ionization energy increases from left-to-right across a column. P is to the right of Si in period 3.

The second ionization energy is the energy required to remove a subsequent (second) valence electron from a singly-charged ion in the gas phase.

The generic second ionization energy equation is: X+(g) ⇒ X2+(g) + e-

The second ionization energy is always larger in magnitude than the first ionization energy for every atom.

The removal of the first electron reduces the electron-electron repulsion energy of the molecule, allowing the positive nucleus to attract the remaining electrons more strongly, increasing the energy needed to remove subsequent electrons.

Atomic radius increases down a column of the Periodic Table.

Each increasing shell can be thought of as another "layer" of electrons, outside the previous layer, increasing the atom's size.

Note: The highlighted elements represent one column of the Periodic Table.

Br

Remember: atomic radius increases going down a column, and Br is below Cl in the halogens column. The valence electrons from Br are in the n=4 shell, those from Cl are in the n=3 shell.

Atomic radius decreases across a row from left to right on the Periodic Table.

This is due to effective nuclear charge. As Zeff increases, the nucleus binds the electrons more tightly, pulling them in closer.

Note: the highlighted elements represent one full row of the Periodic Table.

Si

Remember: Atomic radius decreases from left-to-right across a column, and P is to the right of Si in the Period 3.

The energy released when one valence electron is added to an atom in the gas phase.

The generic electron affinity equation is: X(g) + e- ⇒ X-(g)

Electron affinity increases from left to right across a row of the Periodic Table.

The smaller an atom is, the closer a newly-added valence electron gets to the positively-charged nucleus, and the more energy released when that electron is added.

Electron affinity decreases heading down a column of the Periodic Table.

The further down a column an element lies, the higher the value of n for its valence electrons. Higher n electrons sit further from the atomic nucleus, and so are less bound to the nucleus and release less energy when added.

An atom's electronegativity describes that atom's tendency to attract electron density towards itself through a chemical bond.

Note: electronegativity only applies to atoms in a bond. There is no such concept as the electronegativity of a bare atomic species.

Electronegativity increases from left to right across a row of the Periodic Table.

The smaller an atom is, the closer the electrons in its bonds get to the positively-charged nucleus, and the more strongly the electrons are attracted to the nucleus.

Electronegativity decreases heading down a column of the Periodic Table.

The further down a column an element lies, the larger its radius. This puts more space between the positively-charged nucleus and the electrons in any bonds it makes, reducing the attraction between the nucleus and the electrons.

Fluorine

Electronegativity increases the further right and the closer to the top of the Periodic Table an element is. Fluorine, which is the top-right element that isn't a noble gas, therefore has the highest value of electronegativity.

On the Pauling scale, the most commonly-used scale for determining electronegativity values, fluorine has the highest value possible: 4.0.

Nonmetals are the most electronegative elements.

Fluorine is the element with the highest electronegativity, and as a general rule, the closer an element is to fluorine, the higher its electronegativity.

Some other notes about electronegativity:

The halogens are the most electronegative group.
Noble gases capable of making bonds (Xe and Kr) are relatively strongly electronegative.
Metals, particularly the alkali and alkali earth metals, are generally electropositive (very low electronegativity).

Cl

Remember: electronegativity decreases going down a column, and Br is below Cl in the halogens column.

P

Remember: electronegativity increases from left-to-right across a column, and P is to the right of Si in period 3.

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