Quantum Number and Electronic Configuration

n=2 l subshell ml number of orbitals number of electrons

0,1 2s,2p 0 & -1,0,1 1,3 2,6

n=3 l subshell ml number of orbitals number of electrons

0,1,2 3s,3p,3d 0 & -1,0,1 % -2,-1,0,1,2 1,3,5 2,6,10

Atomic electrons with n=1 n l subshell ml number of orbitals number of electrons

1 0 1s 0 1 2

How many orbitals and electrons are there in the d subshell? orbitals: electrons:

5, 10 For a d subshell, there are five values of (remember the 2 + 1 rule). These values, -2, -1, 0, +1 and +2, correspond to the orbitals dxy, dxz, dyz, dx2-y2 and dz2. Two electrons can occupy each of these orbitals, for a total of ten electrons in the d subshell. In general, the maximum number of electrons in any subshell is 4 + 2.

Group Properties

A column in the periodic table is called a group and, for the representative elements (main group elements, or elements other than transition elements), the group number corresponds to the number of valence electrons of elements in that group. The elements within a group have similar valence shell electron configurations. These are the electrons exposed to other atoms when they react. Some groups have common names. You should be familiar with the group names in the following table for Test Day.

Group I

Alkali Metals

Group II

Alkaline Earth Metals

If an atomic electron has an l-value of 3, what are the possible values for ?

Answer: -3, -2, -1, 0, +1, +2, +3 Do you see a pattern in the above examples? When = 0, there is 1 possible value for ; when = 1, there are 3 possible values for ; when = 3, there are 7 possible values for . In general, for any value of , there will be 2 + 1 possible values for .

Which will fill first, the 4f subshell or the 5p subshell?

Answer: 5 The 5 subshell fills before the 4f subshell because the 5 subshell is lower in energy. Comparing the (n + ) values, the 4f has (4 + 3), or 7, and the 5 is (5 + 1), or 6.

Valence Electrons

As the atomic number increases, the electron configurations become larger and larger. A useful shortcut when writing electron configurations is to abbreviate the inner shell. The inner shell of electrons corresponds to the noble gases, i.e. He, Ne, Ar, Kr, etc., which have filled subshells. The electrons that are not included in the inner shell comprise the outer shell and are referred to as valence electrons. The electron configuration of oxygen, discussed previously, can be abbreviated from 1s22s224 to [He]2s224. Oxygen has six valence electrons (two from the 2s orbital and four from the 2 orbital).

Paramagnetism and Diamagnetism

Atoms, ions, or molecules with unpaired electrons are paramagnetic. Atoms, ions, or molecules with all paired electrons are diamagnetic. These terms may not be defined for you on Test Day, so if you have trouble remembering these definitions a mnemonic may be helpful. Remember the prefix "di-" in diamagnetic means two. A pair of electrons is two electrons, and all electrons in a diamagnetic species are paired. Elements that contain an odd number of electrons are always paramagnetic, but paramagnetism may also exist in substances with an even number of electrons. Let's determine if titanium is paramagnetic or diamagnetic.

Which subshell is higher in energy, or d, assuming the same n value? A. p B. d

B. d Only the quantum numbers n and affect the energy of an orbital. A orbital has a smaller value of ( = 1) than a d ( = 2) orbital does, so the orbital will be lower in energy than the d orbital. The relative energies of orbitals will be discussed more when we get to the electronic configurations of atoms.

Value of l 0 1 2 3

Designation s p d f

Electron Configuration of Ions

Determining the electron configuration of ions is similar to determining the electron configuration of atoms. An ion is formed when an atom gains one or more electrons, to form an anion, or loses one or more electrons to form a cation. To determine the electron configuration of an anion or cation we can usually add or remove an electron, respectively, from the outer orbital of the electron configuration of the element. For example, the electron configuration of carbon, C, is: 1s22s222 To determine the electron configuration of C+, we remove an electron from the outermost shell of carbon - from the 2 orbital. The electron configuration for C+ is: 1s22s221

Orbitals

Electrons move around the nucleus of an atom in volumes of space called orbitals

Magnetic Quantum Number ml

For any given subshell, m (l) can have integer values ranging from -l to +l. Let's look at some examples. If = 0 (an s orbital), ml can have a value of 0. If = 1 (a orbital), ml can have values of -1, 0, or +1.

Group VII

Halogens

Hund's Rule

Hund's rule states that within a given subshell p(, d, or f ) electrons prefer to occupy different orbitals and have parallel spins rather than pair up in the same orbital and have opposite spins. Electrons will fill a subshell with parallel spins before pairing up. Electrons are negatively charged and thus repel one another. Electrons with parallel spins in different degenerate orbitals repel each other less than electrons with opposite spins in the same orbital. Let's look at an application of Hund's rule. The electron configuration of nitrogen is 1s22s223. Hund's rule tells us where the three electrons in the partially filled 2subshell will go; each electron has a parallel spin and occupies a different orbital. The electrons will fill like the diagram on the left: The electrons will not look like the diagram on the right, where an electron occupies the same orbital that another electron occupies, even though there is an empty orbital available. The configuration violates Hund's rule. Note that the electron configuration of nitrogen can also be written as 1s22s22x12y12z1.

Isoelectronic

Isoelectronic species are atoms, ions, or molecules with an equivalent number of electrons. One of the two isoelectronic pairs will always be an ion. For example, the electron configuration of Ne is [He]2s226. The electron configuration of O2- is [He]2s226. The electron configuration of Na+ is [He]2s226. Ne, O2-, and Na+ have the same electron configuration, so these species are isoelectronic with each other.

Group VIII

Nobel Gases or Inert Gases

The Aufbau Principle

Notice how the electrons fill in the lower energy orbitals before they fill in higher energy orbitals. TheAufbau principle or building-up principle, which governs electron configurations, states that electrons fill in the lowest energy orbital first., If we read from left to right across the periodic table, the order of orbitals is: 1s, 2s, 2, 3s, 3, 4s, 3d, 4, 5s, etc. This order is also the order of increasing energy, thus if we fill electrons by reading left to right across the periodic table, we will be following the Aufbau principle.

Pauli Exclusion Principle

The Pauli Exclusion Principle states that no two electrons in an atom can have the same four quantum numbers. A consequence of the Pauli Exclusion Principle is that there can only be two electrons in any given orbital, i.e., the two electrons occupying the z orbital discussed earlier in this workshop. Electrons in the same orbital have the same principal, azimuthal, and magnetic quantum numbers. The only way they can differ is by their spin quantum number. Once we have two electrons (with different spin quanum numbers +1/2 and -1/2) in an orbital, we have exhausted the possible quantum numbers for that orbital.

Orbital Orientation

The magnetic quantum number divides the subshells into individual orbitals and defines the orientation of the orbitals. For an electron with l=1, or in a orbital, ml has three different values: -1, 0, and +1. These three values represent the individual orbitals of the subshell. The orbitals are designated px, py, and pz to specify their orientation. A maximum of two electrons can occupy each pz, py, or px orbital. Therefore, a maximum of six electrons can occupy the subshell.

The Principal Quantum Number n

The principal quantum number, n, gives the overall energy level and size of the electron's path. The allowed values of n are the positive integers: 1, 2, 3,.... As the electron's energy increases, the value of n increases, and the radius of the shell increases -- that is, the electron is, on average, farther from the nucleus. In the figure below, the value of the principal quantum number changes from 1 to 2 to 3. (We will discuss later what the "s" means.) As the value of n increases, you can see how the radius of the orbital increases. The maximum number of electrons per shell is 2n2. For example, no more than 2(3)2 = 18 electrons may reside in the n = 3 shell.

Azimuthal Quantum Number l

The second quantum number used to designate the state of an electron in an atom is the azimuthal quantum number, designated . The azimuthal quantum number refers to subshells, and describes the shape of the electron's orbital. For any given n, the value of can be any integer from 0 to (n- 1). For example, if n = 1, can have a value of 0; if n = 2, can have a value of 0 or 1. In general, for any value of n, there will be n possible values for . While the numerical value of describes the shape of the electron's orbital, values are typically expressed as letters. Below are the standard labels used for the different numerical values of .

Orbital Shape

The value of determines the shape of the subshell. We can expand the table from the previous page to show the shape of the subshells. (The f orbitals have a complicated shape and are not depicted in the table.) Each subshell has a distinct three-dimensional shape where the probability of finding an electron is highest.

Spin Quantum Number ms

The value of mcan be either +1/2 or -1/2. The spin quantum number is responsible for the magnetic properties of an atom, which will be discussed in more detail later. The value of ms has no effect on the energy of the orbital. Typically electrons are depicted as arrows, . If we say that an arrow pointing up has an ms value of +1/2, then an electron depicted as an arrow pointing down, , would have an ms value of -1/2.

Electron Configuration of Transition Metal Ions

Transition metals (the elements of the d block of the periodic table) are a notable exception to the method just described for determining the electron configuration of ions. Transition metals typically form cations, and electrons are removed from the s orbital before they are removed from the d orbital. If we consider the first row of transition metals, the 4s orbital fills before the 3d orbital because the 4s orbital is lower in energy. When electrons occupy these orbitals, however, the 3d orbital becomes lower in energy than the 4s orbital. Electrons are removed from the higher energy orbital, so the electrons are removed from the 4s shell first. For example, the electron configuration of manganese, Mn, is [Ar]4s23d5. Periodic Table Manganese typically forms the Mn2+ ion. The electrons are removed first from the 4s orbital, so the electron configuration of Mn2+ is [Ar]3d5. In the example of Mn2+, the 3d orbital is half-filled (the d orbital holds a maximum of ten electrons). On Test Day, you may forget which oxidation state transition metals ions have, so remember that half-filled and full shells contribute to the stability of ions. For example, cadmium, Cd, a transition metal located in the fifth period, typically forms the Cd2+ ion. The Cd+ and Cd3+ ions are rare; let's work through why this is so. Periodic Table The electron configuration of Cd is [Kr]5s24d10. Loss of two electrons from the 5s orbital would result in a very stable outer electron configuration of 4d10 (a fully-filled d orbital). Loss of one electron and three electrons to form the +1 and +3 ions, would result in the less stable electron configuration of [Kr]5s14d10 and [Kr]4d9, respectively.

The n l Rule

When writing the electron configuration of an atom, it is necessary to remember the order in which subshells are filled. Subshells are filled from lowest to highest energy. The (n + ) rule is used to rank subshells by increasing energy. For example, a 4s orbital has n = 4 and l = 0. Thus, (n + l) = (4 + 0) = 4. A 3d orbital has n = 3 and l= 2. Thus, (n + l) = (3 + 2) = 5. Because the 3d orbital has a higher value of (n + l), it is higher in energy than the 4s orbital. Thus, the 4s orbital will fill before the 3d orbital.

Electronic Configuration

Writing out a series of quantum numbers for the electrons in an atom can be tedious, so a standard method of abbreviating the electronic configuration of an atom is used. We use only the first two quantum numbers, n and , because they indicate the major energy levels. The electronic structure of elements and compounds give rise to the various properties and reactivities that we see in chemistry. Knowing the electronic configuration is the first step to understanding the differences between elements. The periodic table forms the basis for the configuration of electrons.

Quantum theory

claims that any electron in an atom can be described completely by four parameters called quantum numbers. principal quantum number (n) azimuthal quantum number () magnetic quantum number (m) spin quantum number (ms) The first three quantum numbers specify the orbital, and the last one differentiates between the two possible electrons that can occupy the orbital.

What are the principal and azimuthal quantum numbers for an electron in a 4f shell?

n = 4 l = 3 The larger the value of , the higher the energy of the subshell.