2 Electons Electrons: Quantum Numbers, Energy Levels and Electron Configurations

Transcription

1 Electrons: Quantum Numbers, Energy Levels and Electron Configurations For chemical reactions to occur a collision between atoms or molecules must happen. These collisions typically result in an exchange or sharing of electrons. This causes the breaking and making of bonds within molecules. In order to predict the outcome of these collisions and the bond breaking / making, it is vital to know where the electrons are. Unfortunately, the best we can do is estimate the most likely locations for electrons, but this is good enough to understand the properties of atoms that will allow us to do chemistry to create new molecules. Electrons are found in the electron cloud. This is the vast majority of all the space of an atom. The electron cloud is broken into levels. These energy levels begin at the nucleus and work out from there; this is the Bohr Model. The energy levels are subdivided into sections called sublevels. Starting at the nucleus and moving outwards each energy level has one more sublevel than the one that precedes it. Each sublevel is a region of space. This region is vast and so is subdivided into smaller regions of space that contains up to one pair of electrons. These regions are called orbitals, and the orbitals are said to be the most likely location for an electron. Overall the process is to zoom-in starting on the outside of the atom, through the electron cloud, through the energy levels, through the sublevel into an orbital and a possible pair of electrons. Remember that the movement of these electrons between orbitals of atoms that are colliding causes chemistry. Zooming-in: electron cloud energy level sublevel orbital with a pair of electrons. The Bohr model although very useful at times is incomplete and inaccurate. The best way of showing where the electrons are so we can do chemistry is through the use of an Energy Level Diagram. Here are some useful terms for describing an electron as we begin to place them in energy level diagrams. Electron Spin, m s from probability, electrons are said to spin up ( ) or spin down ( ). Note that for quantum numbers: spin up ( ) has m s = + and has m s =. Electron Pair ( ) - combination of a spin up ( ) with a spin down ( ). Pairing requires energy so electrons will be single and pair only if there is no empty orbital of equivalent energy available. See Hund s Rule Energy Level, n A discrete distance from the nucleus. The further the distance, the greater the energy needed for an electron to be located there. Electrons must gain a set amount of energy to move to a higher energy level further from the nucleus (the set amount of energy is said to be quantized). The energy is released as a set amount of energy if the electron moves to a lower level closer to the nucleus. Sublevel An energy level represents a distance from the nucleus, and an orbital is a region of space. As the energy level increases more space is encompassed, so more orbitals are available. The sublevel, a subsection of the energy level, indicates the class of orbital (s, p, d or f) present in that sublevel. Valence electrons These are the electrons in the outermost energy level, and are the electrons involved in bonding and reactions. Electrons are not randomly place into energy levels, but follow set patterns. The basic fundamental rule of this is that lowest energy always is preferred. So if an electron can be at a lower energy level it will be (see Aufbau). Remember electrons are negative and since like charges repel each other the pairing of electrons cost energy. So paring only happens if no other orbitals in that sublevel are available (see Hund s Rule). Lastly, no two particles can occupy the same point in space so only opposite spinning electrons may be in the same orbital (see Pauli Exclusion). Aufbau Principle lowest energy orbitals fill first with electrons (fill diagram from the bottom up, lower energy state is preferred) Hund s Rule of Multiplicity if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them by pairing. Electron pairing requires energy, the lower energy state is always preferred so the electrons stay single. Following the axiom that the lower energy state is preferred the

2 electrons will pair when the choice is pairing or moving to an orbital that is higher in energy Pauli Exclusion Principle no two identical electrons can occupy the same orbital means that only electrons of opposite spin may be in the same orbital Energy level diagrams These diagrams display all the electrons in an atom in their most likely locations (energy level, sublevel and orbital) based on increasing energy. The energy level diagrams can be derived using the Bohr model and the periodic table where each element stands for an electron. (see The periodic table: Energy Level, n, and Sublevels, l below) The following is an empty Energy Level Diagram where each represents an orbital. The notations such as represent the energy level and sublevel. So is the first energy level, s-sublevel. E N 4s 3d 4p E R 3s 3p G Y 2s 2p Once the number of electrons is determined for the given atom, then electrons are placed in the diagram (either spin-up,, or spin-down, ) following the Aufbau Principle (bottom-up), Hunds Rule (no pairing until each orbital in the sublevel has on electron, all single electrons with the same spin) and Pauli Exclusion (orbital pairs are of opposite spin). Example: Draw the energy level diagram for phosphorus, P. Since P has an atomic number of 15 and is neutral it has 15 e s. E N 4s 3d 4p E R 3s 3p G Y 2s 2p Note: the corresponding electron configuration is: 2 2s 2 2p 6 3s 2 3p 3 (see below for more info.) Electron configuration states the arrangement of electrons within the electron cloud; includes the energy level followed by the sublevel then the number of electrons in that sublevel as a superscript. You can think of this as a sort of shorthand notation for the energy level diagram. examples: H = 1 H has 1 electron in the 1 st energy level, s-sublevel. N = 2 2s 2 2p 3 N has 2 e s in the 1 st energy level, s-sublevel 2 e s in the 2 nd energy level, s-sublevel 6 e s in the 2 nd energy level, p-sublevel Please not that all families (vertical columns) have the same valence electron configuration. examples: noble gas (group 18) configuration ns 2 np 6 halogen (group 17) configuration ns 2 np 5 alkali metal (group 1) configuration ns 2 np 4

3 The electron configuration may be determined by the position of the element on the periodic table. (see below) Derivation of the Energy Level Diagrams In deriving the energy level diagram for atomic orbitals it is convenient to use the periodic table as a model of the atom. In this model, each element represents a potential electron and each period (horizontal row) represents an energy level. The sections of the periods represent the sublevels. Note that to it is also convenient to move He next to H to put 2 elements (electrons) in the sublevel. (See below.) l = 0 The periodic table: Energy Level, n, and Sublevels, l n = 1 l = 1 n = 2 2s 2p n = 3 3s l = 2 3p n = 4 4s 3d 4p n = 5 5s 4d 5p n = 6 6s 5d 6p n = 7 7s 6d 7p The Periodic Table with the s,p and d-blocks broken into sublevels, l = 0, 1, 2. The f-block is not shown. Note that within a specific block the l-value is constant no matter what the value is for the energy level, n. For example, in the, l = 0 and in the 5s still l is 0. The number of sublevels per level is determined by the relationship of l with n. Since: l = 0, 1,, (n-1) where l is the sublevel and n is the energy level, there is always a gain of one sublevel for every increase in energy level. That is 1 st energy level has one sublevel,, the 2 nd energy level has two sublevels, 2s and 2p etc. This can also be seen via the layout of the periodic table (see above). Thus, we can convert the Bohr-Model of the atom to a graph with energy on the y-axis and then subdivide each energy level into the proper amount of sublevel to create the following. E n = 4 E 4s 3d 4p N N E n = 3 E 3s 3p R R G n = 2 G 2s 2p Y Y n = 1 Bohr-Model (rings are energy levels) graph of energy levels graph of energy levels split into sublevels Once again, this matches what we see in the periodic table. Each horizontal row of the periodic table is like an energy level and each block of the periodic table is like a sublevel. The only breakdown in this analogy is for the center of the table the d-block (d-sublevel) where l = 2 the d s are actually part of the previous energy level. Which is why it is the 3d in row n=4 and not the 4d etc.

4 Finally, it is time to draw the Energy Level Diagram. The last step is to divide the sublevels into specific orbitals. Knowing that an orbital can hold up to 2 electrons (1 pair), we can add sublevels to our graph. Usng the periodic table as our guide and knowing that an element represents an electron, we have s-sublevel 2 elements per row, 2 electrons, 1 pair so 1 s-orbital p-sublevel 6 elements per row, 6 electrons, 3 pairs so 3 p-orbitals d-sublevel 10 elements per row, 10 electrons, 5 pairs so 5 d-orbitals f-sublevel 14 elements per row, 14 electrons, 7 pairs so 7 p orbitals (block at the bottom of the periodic table) E E N 4s 3d 4p N 4s 3d 3p E E R 3s 3p R 3s 3p G G Y Y 2s 2p 2s 2p graph of energy levels split into sublevels graph of sublevels split into orbital. This is an Energy Level Diagram Confused? The atom is like an office building where each floor going up is bigger than the one below. Each floor is like an energy level. In a building the floors are divided into rooms. So each room is a sublevel. In each room is a loveseat to hold two opposite people. So each loveseat is an orbital containing up to two opposite spinning electrons. Much like in real life where people may or may not be in the room, the orbitals are only probable locations where the electrons may or may not be. Quantum Numbers In deriving the energy level diagram for atomic orbitals we showed that electrons have spin and pair with an electron of opposite spin and that the most likely location for an electron is in an orbital which is contained in a sublevel, which is part of an energy level which is part of the electron cloud. Therefore an electron has four main characteristics to describe it and its most likely location within the electron cloud: 1 st energy level, n 2 nd sublevel, l 3 rd orbital, m l 4 th spin, m s These four characteristics are called quantum numbers and placing then in a set creates a set of quantum numbers. The set always has the format { n, l, m l, m s }. Each quantum number has a numerical equivalent. Energy Level, n A discrete distance from the nucleus. The further the distance, the greater the energy needed for an electron to be located there. Possible values for n: n = 1, 2, 3,

5 Sublevel, l The number of sublevels found in an energy level maybe determined by the relationship: l = 0, 1,, n-1 where l is the sublevel and n is the energy level. For example, if n = 1 then l = 0 so there is one sublevel ( s ) in the 1 st energy level if n = 2 then l = 0 or 1 so there are two sublevels ( s, p ) in the 2 nd energy level Orbitals, m l A defined region (shape) of space, where it is most probable to find an electron. Each orbital contains 0, 1, or 2 e s. There are four types of orbitals: s, p d, f (one for each sublevel, l = 0,1,2,3). The number of orbitals within each type (sublevel) is determined by the values of m l, where m l = - l, to, + l. (see below) For instance each p-orbital has an hourglass shape and is aligned along an axis of space the p-orbital has 3 types: p x, p y, p z.. The classes of orbitals are: l = 0 s: 1 type, total of 2 e s, 1 pr m l = 0 l = 1 p: 3 types, total of 6 e s, 3 pr s m l = -1, 0, or +1 l = 2 d: 5 types, total of 10 e s, 5 pr s m l = -2, -1, 0, +1 or +2 l = 3 f: 7 types, total of 14 e s, 7 prs m l = -3, -2, -1, 0, +1, +2, or +3 Note: each value of m l represents each type of orbital. e.g. for those p- orbitals mentioned earlier: p x, p y, p z, there are values -1, 0, +1. Electron Spin, m s from probability, electrons are said to spin up ( ) or spin down ( ). Note that for quantum numbers: spin up ( ) has m s = + and has m s =. Transitions between States Example: Assign the set of quantum numbers for this electron: Because the electron is in a 3p sublevel: n= 3 and l = 1. Additionally the center p-orbital is typically m l = 0, Spin up so m s = + Overall the set of quantum numbers would be {3, 1, 0, + } An electron absorbs energy in the ground state. With the gain of energy the electron must move-up to an energy level that matches that new energy. This creates an excited state. Lower energy states are preferred. The electron emits the absorbed energy as a photon (particle) of light and relaxes (falls) back to the ground state. Note that this is exactly the process by which things glow in the dark and how neon signs work. Here are some useful terms that we will be using to discuss this process. Ground State All electrons in the lowest energy level possible. Excited State One or more electrons at an energy higher than the ground state. Excitation The process of absorbing energy which moves an electron to an excited state. The energy source may vary widely for example to get something to glow in the dark the source is light. Relaxation The process of releasing energy as an electron falls from an excited state to a lower energy state. The energy is released as a photon of light which may or may not be visible (depends on the wavelength, : E = hc/ where h is 3p

6 Plank s constant, 6.6x10-34 J. s, and c is the speed of light in a vacuum, 2.998x10 8 m/s) Example: Transition from the Ground-state to an Excited State then Back to Ground An electron absorbs energy in the ground state. With the gain of energy the electron must move-up to an energy level that matches that new energy. This creates an excited state. Lower energy states are preferred. The electron emits the absorbed energy as a photon (particle) of light and relaxes (falls) back to the ground state. Note that this is exactly the process by which things glow in the dark and how neon signs work. Atom Stability Electronic E E E N n=4 N n=4 N n=4 E E E R n=3 R n=3 R n=3 G G G Y n=2 Y n=2 Y n=2 n=1 n=1 n=1 ground excitation excited relaxation ground energy is absorbed energy is emitted The term electronic refers to the arrangement of electrons in the electron cloud. Please remember that lower energy states are always preferred, so lower energy states are stable. In terms of electrons the most stable states occur when all energy levels are either completely full or completely empty. So consequently atoms will gain electrons (anions) to fill energy levels or lose electrons (cations) to empty energy levels. Example: N = 2 2s 2 2p 3 N will gain 3 e s to fill the 2 nd s and p, becoming N 3- with 2 2s 2 2p 6 Nuclear B = 2 2s 2 2p 1 B will lose 3 e s to empty the 2 nd s and p, becoming B 3+ with 2 2s 0 2p 0 When a nucleus is unstable it will release matter and/or energy to become stable. The released matter/energy is radiation, and the process of releasing the matter/energy is called radioactive decay. There is no set rule for stability, but evaluating the neutron to proton ratio for all known isotopes, it can be seen that stability n n occurs when the is near 1, and that the further the value of is from 1, the more likely the isotope will be unstable and thus radioactive. Example: p Which isotope is likely to be radioactive? 12 6 C 13 6 C 14 6 C p n p = furthest from 1, so most likely radioactive The chemical reaction associated with the release of matter and energy from the nucleus during radioactive decay are called Nuclear Transformation Reactions. These reactions constitute the various types of radioactive decay. The rate at which these reactions occur is based upon the Half-Life of the radioactive isotope. The Half-life is the time it takes for half of a sample of a radioactive isotope to decay. Example: The half-life of 32 P is 14 days. So after 14 days a 50 g sample of 32 P is now 25 g of 32 P and 25 g of 32 S. After another 14 d the sample is 12.5 g of 32 P and 37.5 g of 32 S (see beta decay below)

7 The following are the types of radioactive decay. The energy and stability of each nucleus is unique; leading to different nuclei doing different radioactive decay reactions. Typically a nuclei will lose neutrons or protons based upon the n:p ratio. For example a nuclei that is high in neutrons will undergo beta decay while one that is high in protons will undergo positron emission. This can be seen in the two isotopes of phosphorus, P and P, below. Large nuclei will often lose mass through alpha decay (loss of 2n and 2p). Remember, lower energy states are preferred, so the path of radioactive decay that leads to the lowest energy stability, n,close to 1 will be taken. p o, Alpha Particle, He positive He nucleus ejected from the nucleus, Fr He + At 85 o Beta Decay, o 0 * 0, Gamma Rays o Positron Emission, o EC-electron capture Example: e high energy e - is ejected from the nucleus ( 1 n 1 p + 0 e ), 32 P e S e high energy photon emitted as nucleus moves from excited to lower energy state 232 * Th Th + 0 * 90 0 (* means high energy, excited state) positive particle ejected from nucleus ( 1 1 p 1 0 n P 0 e + 30 Si e 1 ) e - falls into the nucleus combining with a proton and forming a neutron, 202 Tl + e Hg Determine the missing particle. State the type of radiation. (The sum total of atomic mass (top number) must be the same on both sides. Same with the atomic numbers (bottom number). Then write the symbol that matches the atomic number. I 0 e ans: Xe, beta decay 82 Sr 78 Kr + ans: He, alpha decay

8 alkali metals Noble gases halogens c h a l c o g e n s alkaline earth metals 3 Periodic Table History Dmitri Mendeleev Henry Mosely Periodic Law Layout Period Group/Family Wrote the 1 st periodic table based on increasing atomic mass and similar properties. Left gaps where necessary in order to line-up families with similar properties. Predicted products of missing elements that, when discovered, would fill-in the gaps Created the modern periodic table based on increasing atomic number The physical and chemical properties of the elements are periodic functions of their atomic number. Horizontal rows A period is likened to an energy level when completing energy level diagrams. Moving left to right, the effective nuclear charge (total protons kernel electrons) increase causing the attraction between each valence electron and the nucleus to increase, this causes the atomic radius to decrease, and electronegativity and ionization energy to increase. A vertical column Elements in the same family have the same valence e-config, and thus similar properties When moving down a group the distance (# of energy levels) between the nucleus and each valence electron increase causing the attraction between them to decrease, so atomic radius increases down a group while the electronegativity and ionization energy decrease. Names Group 1 Alkali Metals Group 2 Alkaline Earth Metals Group 16 Chalcogens Group 17 Halogens Group 18 Noble Gases Overall layout of the periodic table metals nonmetals Transition metals Rare Earths Lanthanides actinides

9 Trends Electron shielding Effective nuclear charge Example: the masking of the nucleus by the kernel electrons. Shielding is constant within a period, but grows down a group the charge felt by each valence electron. Calculated by protons kernel electrons Increases left to right across a period, but is constant in a group 7 Li eff. nuclear charge is 1+ (3p s with 2 kernel e s), valence is 3 2nd level 19 9 F eff. nuclear charge is 7+ (9 p s with 2 kernel e s), valence is 2nd level So, each valence electron on F feels a 7+ charge while each valence electron for Li only feels a 3+ charge. That is why F has the greater attraction between each valence electron and the nucleus. Attraction attraction between each valence electron and the nucleus trend = Moving left to right across a period, the effective nuclear charge (total protons kernel electrons) increases causing the attraction between each valence electron and the nucleus to increase, this causes the atomic radius to decrease, and electronegativity and ionization energy to increase. When moving down a group the distance (# of energy levels) between the nucleus and each valence electron increase causing the attraction between them to decrease, so atomic radius increases down a group while the electronegativity and ionization energy decrease. Electronegativity the ability to attract electrons in a covalent bond trend = First Ionization Energy the energy needed to remove one electron trend = Atomic Radius distance from the nucleus to the valence energy level trend = examples: Which is more electronegative, K or Cl? ans = Cl Which has the larger atomic radius, S or As? ans = As