## Electronic Structure

### Orbital structure of hydrogen atom

The hydrogen atom possesses only one electron and one electron shell. Based on the quantum mechanics model of atoms, this means that Hydrogen’s subshell is the 1s subshell. The s orbital is spherical in shape.

#### Principal quantum number, n

The principle quantum number, n, describes the highest energy level for an atom of a particular element. The highest energy level corresponds to the number of electron shells an atom has. The easiest way to identify an element’s principle quantum number is by observing the period it is in (a.k.a. the row); i.e. Hydrogen is in period (row) 1, so it’s n value is 1. This value of n=1 tells us that Hydrogen has only one subshell.

#### Number of electrons per orbital (hydrogen)

Within each shell (n), there are exactly 2n^{2} electrons. Within each orbital, there can be a maximum of only 2 electrons. Hydrogen does not have two electrons, it has one electron (given by it’s atomic number, 1).

**Reminder**: A Hydrogen cation (H^{+1}) has no electrons.

### Ground state, excited states

An atom of any element is said to be at its ground state when it is at its lowest energy potential. This means that all the electrons are in their expected shells, sub-shells and orbitals, as determined by the quantum mechanical model of atoms.

An atom’s electrons may be excited in the presence of energy (heat, light, radiation, etc.). The term excited refers to the movement of one electron from a lower energy level (shell) to a higher energy level. In terms of quantum numbers, an electron is excited when the principle quantum number (n) has increased; i.e. from n=1 to n=2.

In order to excite an electron to a higher energy state, the energy must be specific. Technically, the energy must be quantized. Moving an electron from one energy level to a higher energy level is equal to the difference in energy between the two energy levels.

Although this is mostly covered in the Physics section, it is relevant to note that the amount of energy needed to excite an electron from the first shell to the second shell is equal to E_{n2} – E_{n1}.

h*v* = ΔE = E_{n2} – E_{n1} = -13.6 eV -(-3.40 eV) = -10.2 eV

**Remember**: The amount of energy required to move from a higher energy level (n=2) to an even higher level (n=3) is significantly smaller than the amount of energy required to excite an electron from the ground state.

E_{n3} – E_{n2} = -3.40 eV -(-1.51 eV) = -1.89 eV

### Absorption and emission spectra

The absorption spectrum represents the the energy required to excite electrons in an element in terms of wavelength and frequency (E = hf = hc/λ ). The energy required to excite every electron present in an element from the ground state to an excited state is unique to that element. Absorption is graphed as intensity versus wavelength. More information can be found (soon) in the Physics section. The color we perceive of any element is due to the colors which are not absorbed.

**Random Factoid**: Absorption spectra are used to identify gases present in stars.

Hydrogen absorption and emission spectrum

The Emission spectrum is the exact opposite of the absorption spectrum. It represents the amount of energy released by an excited election when transitioning to a lower energy level. The energy released is a photon with the same amount of energy required to excite the electron (see section Ground State versus Excited State) and the electromagnetic energy of the photons is equal to hc/λ. Each photon released by an electron has a characteristic wavelength, specific to the energy transition. Because the energy release is quantized, a continuous spectrum is not observed — instead a line spectrum is seen.

There are many wavelength series, but we should familiar with these two: the Lyman series in the ultra-violet (n = 2 to n = 1), and the Balmer series in the visible spectrum (n = 2 to n = 3). The Lyman series has a wavelength of 1250-800 where the Balmer series has a wavelength of 800-400 nm.

The equation used to calculate the energy absorbed or emitted is:

E = h*v* = -R_{H}[(1/n^{2}_{initial}) – (1/n^{2}_{final})]

*v* = c/λ

**Remember: **If the E value is positive, it represents absorption energy. If the E value is negative, it represents emission energy.

### Quantum numbers n, l, m, and s

Quantum numbers are used to describe electron configuration and probable electron locations of an atom. The Quantum model of an atom replaced the Bohr model; but the Bohr model laid the path for the QMofA.

The **quantum number n** represents the principle quantum number. The principle quantum number describes the highest energy level possible for an electron in any atom. Basically, the number tells us how many electron shells are present in an atom. In addition, the n number tells us the relative size of the atom’s radius (n = 1 being the smallest).

**Quick refresher**: Atomic shells contain subshells. Subshells contain orbitals. The first atomic shell has one subshell, 1s. The second atomic shell has 2 subshells: the 2s and 2p. Orbitals within subshells are represented as, in the case of the p orbital, p_{x}, p_{y}, and p_{z}. Each orbital can only hold two electrons.

The value of n is given by the period (row) that an element is located in on the periodic table of elements.

Hydrogen, n = 1 (first period)

Florine, n = 2 (second period)

Chlorine, n = 3 (third period)

**Remember**: As n increases, so does the atomic radius. This is also true when an electron is excited — the radius expands and then contracts when the electron returns to the ground state.

From the principle quantum number, n, we are able to distinguish the other quantum numbers:

*l* = 0 to (n – 1)

**Quantum number ***l* (Azimuthal) represents the number and shape of subshells within a shell (aka energy level). For example:

Hydrogen, n = 1, *l* = 0 to (1 – 1) = 0

**IMPORTANT**: Although the value of *l* is zero, it is important to realize that the value 0 is a digit. A single digit, 0, represents the first subshell — the s subshell. This means that Hydrogen (or any other atom with a n value of 1, such as Helium) only has one orbital, the 1s orbital. The s orbital is spherical because it does not share space with any other subshells (no repulsion).

Another example: Florine, n = 2, *l* = 0 to (2 – 1) = 0, 1

Here there are two digits, 0 and 1. As with the example of Hydrogen, the 0 digit represents the shell’s s orbital. The second digit, 1, represents the the second orbital within the shell — the p orbital.

Because we are using the n value of 2, the orbitals are called the 2s (represented by the 0) and 2p orbitals (represented by the 1). The first shell containing the 1s orbital is not accounted for (it’s considered a given).

The **quantum number m**_{l} (also known as the **quantum number m**) represents the number of subshells present in each orbital. Although at first glace it seems very similar to the *l* quantum number, the m_{l }** **number does not count the number of orbitals present in a shell, it distinguishes electron paths (aka subshells) within the s, p, etc. orbitals.

**m**_{l }= –*l* to *l*

Tricky example:

Chlorine, n = 3, *l* = 0, 1, 2

There are three *l* values to derive m_{l}, *l* = 0, *l* = 1, and *l* = 2

For the s orbital (*l* = 0), m_{l} = 0.

As with the previous quantum number l, the 0 value represents one digit. Hence, there is a *maximum* of one subshell within the s orbital.

For the p orbital (*l* = 1), m_{l} =-1, 0, 1

Here we have three digits, -1, 0, and 1. This indicates that there are a *maximum* of 3 subshells located in the p orbital.

For the d orbital (*l* = 2), m_{l} =-2, -1, 0, 1, 2

Here we have five digits, -2, -1, 0, 1, and 2. This indicates that there are a *maximum* of 5 subshells located in the d orbital.

However, Chlorine does not have a d orbital.

**REMEMBER**: Quantum numbers do not dictate the number of electrons, orbitals or subshells of any particular element. They represent the highest energy level possible for a given principle quantum number (an atomic shell).

Chlorine has a 3rd shell. It’s principle quantum number is 3. However, Chlorine’s 3rd shell does not contain a d orbital, as postulated by the **Aufbau principle** which states, “According to the principle, electrons fill orbitals starting at the lowest available (possible) energy states before filling higher states (e.g. 1s before 2s).” This means that the 3s and 3p orbitals will be filled before the 3d orbital — which explains why Chlorine does not have a d orbital; it does not have enough electrons to occupy the s, p and d orbitals of the 3rd shell.

The **m**_{s} quantum number (a.k.a. the **s quantum number**) represents the spin state for each electron pair, and hence the maximum number of electrons allowed in each subshell. Before we had mentioned that each subshell could only contain two electrons. In addition, the electrons cannot have the same spin orientation, otherwise they would repel each other and fail to stay in the same subshell. The spin states are given a value of +1/2 and -1/2. *The value of m*_{s }will always be +1/2 and -1/2 which are represented as up and down arrows. **This is the basis for orbital diagrams**.

Example:

Hydrogen, n = 1, l = 0, m_{l} = 0, m_{s} =+1/2, -1/2

In the diagram, the number 1 represents the shell number (n), the s represents the orbital (l), the box which contains the arrows represents the number of subshells (m_{l}), and the two arrows represent the opposite spin states (m_{s}).

**REMEMBER**: An electron diagram is a visual representation of the atomic numbers.

### Number of electrons per orbital

The number of electrons per orbital is determined by the number of subshells in a orbital (m_{l}) quantum number, multiplied by 2 (representing the two states of m_{s}).

### Conventional notation for electronic structure

The conventional notation for electronic structure is synonymous with *electron configuration diagrams*. Electron configuration diagrams are based on the quantum numbers n, l, m, and s.

In order to properly create an electron configuration diagram, one needs to remember the order of permitted energy levels within an electron — 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, etc. Or, creating a electron configuration scheme, such as this:

(C) MDHS SCH 4U Study Page

This video also covers electron configuration diagrams:

[yframe url=’http://www.youtube.com/watch?v=5N6JYY_QDw8′]

**REMEMBER**: To write the ground state electron configuration of a cation, remove electrons from the highest occupied energy level in the ground state electron configuration of the atom. In other words, remove electrons from the orbital with the highest principal quantum number.

Na: 1s2 2s2 2p6 3s1 Na+: 1s2 2s2 2p6

Mg: 1s2 2s2 2p6 3s2 Mg2+: 1s2 2s2 2p6

Fe: 1s2 2s2 2p6 3s2 3p6 4s2 3d6

Fe2+: 1s2 2s2 2p6 3s2 3p6 3d6

Fe3+: 1s2 2s2 2p6 3s2 3p6 3d5

### Bohr atom

Bohr was the first to propose a model of the atom which had a densely packed nucleus of positive charge, surrounded by electrons revolving around the nucleus in a defined pathway (orbits) with distinct energy levels. He also identified that electron excitation in Hydrogen was only possible at certain frequencies. This gave rise to the concept of quanta — discrete energy bundles. He proposed that electrons could be excited only when a specific amount of energy was supplied to the electron.

E = h*f*

Bohr used quantum mechanics to define the angular momentum of an electron (quantum number *l*), and found that the momentum of an electron changes only in discrete amounts in respect to the principle quantum number. Hence, the energy emitted (or absorbed) by an electron is quantized by the principle quantum number.

**REMEMBER**: As the principle quantum number increases, energy increases and get closer to zero.

### Effective nuclear charge

Electrons surrounding a nucleus experience two major forces: the force of attraction to the positive nucleus, and the repulsion from neighboring electrons. Electrons at lower energy levels shield or offset the attractive forces experienced by valence electrons. The resulting attractive force (real attraction minus the shielding effect) is termed the **effective nuclear charge**. Effective nuclear charge allows valence electrons to bond to other atoms, or create ions.