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The Modern Model of the Atom History of the Atomic Model • Democritus (400 B.C.) • Believed that matter was composed of invisible particles of matter he called atoms. • Antoine Lavoisier (1700’s) • Law of Conservation of Mass – Matter is not created or destroyed. • Joseph Proust (1700’s) • Law of constant composition – compounds are composed of atoms in definite ratios. History of the Atomic Model • John Dalton (Late 1700’s) • First atomic theory explaining chemical reactions • J.J. Thomson (1897) • Discovered the electron using cathode ray tubes • Robert Millikan (1909) • Found the charge and mass of the electron in his famous “oil-can” experiment. In Bohr’s atom (1913), electrons had a single energy state, described by its Principle Quantum Number, corresponding to an orbit at a specific distance from the nucleus as observed from the spectral lines of hydrogen. However, It was soon discovered that electrons could not be described so simply. Experimental data began to suggest that not all electron energy levels fit into nice and neat integers. History of the Atomic Model • Ernest Rutherford (1911) • Discovered the nucleus, and later the proton, in his famous “gold foil” experiment. • James Chadwick (1932) • Discovered neutrons studying atomic masses. • Neils Bohr (1913) • His atomic model accounted for the atomic emission spectrum of the hydrogen atom History of the Atomic Model • Arnold Sommerfeld (1916) • • Used Einstein's Theory of Relativity to expand Bohr’s single electron orbit into two possible electron orbits that an electron can attain to explain the “Fine Structure” of the hydrogen line spectrum, or the doubling of the spectral lines. Electrons were then thought to not only have a principle energy, but also could exist with different sub-energies. • Eventually, Sommerfeld introduced a second quantum number, the Azimuthal Quantum Number, to describe the angular momentums of an electron giving rise to the observed Fine Structure of hydrogen. 1 History of the Atomic Model History of the Atomic Model • Arnold Sommerfeld (1916) • Samuel Goudsmit [top] and Geroge Uhlenbeck (1916) • • • • Accounted for how a magnetic field affects the Fine Structure by widening the gap between the spectral lines of hydrogen, known as the Zeeman Effect. This led them to the understanding that electrons must have a spin property and that spin will affect the energy of the electron as it moves around the nucleus. The result was the inclusion of a third quantum number, called the Magnetic Quantum Number, to describe further divisions in electron energies. However, the Zeeman Effect could not be explained. History of the Atomic Model • Wolfgang Pauli (1924) • • • proposed a new quantum number, Spin Quantum Number, with two possible values in order to resolve inconsistencies between observed molecular spectra and the BohrSummerfeld model. This brought the total quantum numbers required to describe the energy of an electron to four. Formulated the Pauli exclusion principle which stated that no two electrons could exist in the same quantum state; meaning, no two electrons can have the same set of four quantum numbers. History of the Atomic Model • Louis de Broglie (1924) • Introduced the Wave Theory of Matter where he proposed that all moving particles, particularly subatomic particles such as electrons, exhibit a degree of wave-like behavior. h mv Where: m = mass v = velocity h = planck’s constant Equation sheet • • • Added elliptical orbits to the Bohr model to explain the apparent discrepancy between Bohr’s single electron energy state and the noninteger energy levels being observed from spectral data. Electrons in these “elliptical” orbits would have energies more in line with the experimental evidence being collected and were described rather nicely by the two new quantum numbers; Azmuthal and Magnetic. The inclusion of elliptical orbits into “shells” of electrons made the model very difficult to use, and it still couldn't explain more complex atoms. Nor could it explain the Zeeman Effect. Electron Shell Model Collectively, the Rutherford-Bohr model and the Bohr-Summerfeld model are referred to as “Old-Quantum Theory,” or more commonly the Electron Shell Model. Where the Rutherford-Bohr model predicted circular obits described by a single quantum number, the Bohr-Summerfeld model describes electron orbits that are elliptical and require three quantum numbers. However, they had one thing in common, they depended solely on the particle nature of electrons. History of the Atomic Model • Erwin Schrödinger (1926) • • fascinated by de Broglie's idea, Schrödinger explored whether or not the movement of an electron in an atom could be better explained as a wave function rather than as a point particle in his famous equation. This approach elegantly predicted many of the spectral phenomena that Bohr's model failed to explain. h2 2 2 2 2 2 V E 8 2 m x 2 y z Where: V = potential energy of electron E = total energy of electron = wave function of electron 2 History of the Atomic Model • Max Born (1926) History of the Atomic Model • Werner Heisenberg (1927) • A consequence of describing electrons as waveforms is that it is mathematically impossible to simultaneously derive the position and momentum (mν) of an electron. • The Heisenberg Uncertainty Principle: • • • proposed that Schrödinger's wave function described not the electron but rather all its possible energy states, and thus could be used to calculate the probability of finding an electron at any given location around the nucleus. He formulated the now-standard interpretation of the probability density function for ψ2 in the Schrödinger equation. This reconciled the two opposing theories of particle versus wave electrons and the idea of wave–particle duality was introduced. This theory stated that the electron may exhibit the properties of both a wave and a particle. x m v h 4 • The Uncertainty Principle invalidated Bohr's model, with its neat, clearly defined circular orbits and ushered in the newly emerging Quantum Mechanics Model of the atom. New-Quantum Theory Quantum Mechanic Atomic Orbitals • Electrons behave as waves in their motions around the nucleus. • The question then becomes how do the electron wave functions and probability distributions translate into 3-D spaces according to the Quantum Numbers used to describe them? • An electron’s wave function (ψ) is found by the Schrödinger Equation and describes its energies corresponding to the four quantum numbers. ψ is a function of distance (Principle Quantum Number) and angular momentum according to its vector components (Angular-Momentum Quantum Number and Magnetic Quantum Number). Each ψ corresponds to a region of space within which an electron is found, called an orbital. • does NOT describe the exact location of the electron. No one orbital may contain more than two electrons and they must be of opposite spin (Spin Quantum Number). • ψ 2 is proportional to the probability of finding an e- at a given point. 1. Principal Quantum Number, n • The principal quantum number, n, describes the principle energy level in which the electron resides. • The values of n are integers ≥ 1. • The energy of the level increases away from the nucleus • Answer: The Principle Quantum Number gives us the overall size of the electrons probability density; distance from the nucleus. The Azmuthal Quantum Number (Angular-Momentum) describes the number of probability densities at any given main energy level; the number and shapes of electron sublevel energies. The Magnetic Quantum Number tells us how many orientations a particular set of probability densities will have within each sublevel; the number of electron orbitals. The Spin Quantum Number denotes the spin an electron will have in any one orbital. 2. Azimuthal Quantum Number, l • This quantum number defines the sublevels and the shape of each orbital in the sublevels in each principle energy level. d Sublevel p Sublevel Principle Quantum # Azimuthal Quantum # 1 s 2 s p 3 s p d 4 s p d f s Sublevel 3 3. Magnetic Quantum Number, ml • Describes the number of orbitals in each sublevel and the threedimensional orientation of each orbital. Sublevel # Orbitals s 1 P 3 d 5 f 7 The s Sublevel has only one s Orbital • Spherical in shape. • Radius of sphere increases with increasing value of n. The p Sublevel has 3 Orbitals • Each p orbital has two lobes with a node between them. • The shape of a p orbital is known as dumbell. The d Sublevel has 5 Orbitals • Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center. •There are 7 f orbitals •The f orbitals are much to complicated to represent graphically. 4 4. Spin Quantum Number, ms • The “spin” of an electron describes its magnetic field, which affects its energy. • The electron spin is either +1/2 or -1/2. •From our understanding of the quantum model, we can describe the location of each electron around the nucleus of an atom. Principle Quantum # Azimuthal Quantum # AngularMomentum Quantum # # electrons per sublevel # electrons per main energy level 1 s s 2 2 2 s p s px,py,pz 2 6 8 3 s p d s px,py,pz d1,d2,d3,d4,d5 2 6 10 18 4 s p d f s px,py,pz d1,d2,d3,d4,d5 f1,f2,f3,f4,f5,f6,f 2 6 10 14 32 7 Electron Configurations According to the Quantum Molecular Model Electron Configurations Therefore, 4th main energy level or n = 1 Electron Configurations Therefore, p sublevel in the 4th main energy level • Distribution of all electrons in an atom • Consist of – Number denoting the energy level – Letter denoting the type of orbital • Distribution of all electrons in an atom • Consist of – Number denoting the energy level Electron Configurations • Distribution of all electrons in an atom. • Consist of – Number denoting the Therefore, 5th energy level. electron of the – Letter denoting the possible 6 filling type of orbital. the 3 orbitals of – Superscript denoting the p sublevel in the number of electrons in those the 4th main orbitals. energy level 5 Three rules guide the filling of electrons in the main energy levels, sublevels and orbitals to determine the electron configuration of an atom: Aufbau principle: States that electrons will occupy the lowest possible energy level possible. This gives rise to the Order-of-Fill: 1.Aufbau principle 2.Pauli Exclusion Principle 3.Hund’s Rule. Following the arrows on the diagram gives rise to the following Order-of-Fill: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p 8s •Notice, 4s is lower in energy than 3d and fills first. Using the order of fill, we can designate the electron configuration for any element. Observe: Given that an s orbital only holds 2 electrons, p orbital holds 6 electrons, d holds 10 and f holds 14, the electron order of fill also designates the number of electrons in each sublevel: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6 8s2 1.Use the order of fill to write the electron configuration for the following elements: •Chlorine has 17 electrons in its electron cloud Nitrogen •From the order of fill: Sulfur 2 + 2 + 6 + 2 + 5 = 17 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6 8s2 Magnesium Potassium Krypton •Therefore: 17Cl 1s2 2s2 2p6 3s2 3p5 6 A second method of writing electron configurations, know as orbital fill notation, shows not only the main energy level, sublevels and electrons in each sublevel, but also includes the individual orbitals. • Each box represents one orbital. • Half-arrows represent the electrons. • The direction of the arrow represents the spin of the electron. To write electron configurations using the orbital fill notation, the Pauli Exclusion Principle and Hund’s Rule must be followed. HUND'S RULE • According to Hund's rule, electrons will not join So, where electron configurations look like: 1s2 2s2 2p5 9F Orbital fill looks like: 9 F 1s 2s 2px 2py 2pz THE PAULI EXCLUSION PRINCIPLE • An atomic orbital may describe at most two electrons, each behaving as if they spin on an axis. • According to the Pauli exclusion principle, only electrons spinning in opposite directions can occupy the same orbital within a sublevel. other electrons in an orbital of a sublevel if an empty orbital of the same energy is available in the sublevel. •Thus, the second electron entering a p sublevel will go into an empty p orbital of the sublevel rather than into the orbital that already contains an electron. 2. Use the order of fill to write the orbital fill notation for the following elements: The question now becomes: Sulfur Why is it so important to know the location of electrons around the nucleus of the atom? Magnesium The answer? Nitrogen Potassium Krypton Valence electrons Valence electrons are the electrons located in the highest main energy level (or valence shell) of an atom. 7 Notice: Group 2 atoms had how many valence electrons? Group 3? Group 7? Group 8? What trend can be identified on the periodic table related to valence electrons? What about the transition metals (d and f block elements)? Electron Distribution in Molecules G. N. Lewis 1875 - 1946 Valence electrons (the outer most electrons) are responsible for the interaction between atoms when forming chemical compounds. Another way to say that is that valence electrons are the electrons that participate in chemical bonding. The Octet Rule explains that every atom seeks a full valence shell. It is the attaining or loss of valence electrons that will satisfy the octet rule. For example: • Valence Electron distribution is depicted with Lewis electron dot notation Electron Dot Notation shows the number of valence electrons of an atom around the atoms nuclear symbol. Oxygen has 6 valence electrons (group 6) 16 8 O or for convenience O 1. When assigning valence electrons to an atomic symbol, each side of the symbol should receive one electron before a second electron is placed on a side. 2. Always assign electrons across from each other when possible. Obtain the number of valence electrons for each of the following atoms from its group number and draw the correct Electron Dot Notation (a.k.a. Lewis Dot Structures). 1. 2. 3. 4. 5. K N Cl B Be 6. S 7. C 8. Ar 9. P 10.H Write the electron configuration and orbital fill notation for each atom on the periodic table from element 1 (H) to element 36 (Kr). 8