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Quantum Theory and Atomic Structure
Chapter Quantum Theory and Atomic Structure
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Learn from yesterday, live for today, hope for tomorrow
Learn from yesterday, live for today, hope for tomorrow. The important thing is not to stop questioning. Albert Einstein
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Light Made up of electromagnetic radiation.
Waves of electric and magnetic fields at right angles to each other. There are many different l and f. Radio waves, microwaves, x rays and gamma rays are all examples of EM radiation. Light is only the part our eyes can detect. Gamma rays Radio waves
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Low energy High energy Radiowaves Microwaves Infrared . Ultra-violet X-Rays GammaRays Low Frequency High Frequency Long Wavelength Short Wavelength Visible Light
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In 1900’s Matter and energy were seen as different from each other in fundamental ways. Matter was particles. Energy could come in waves, with any frequency. Max Planck found that the cooling of hot objects couldn’t be explained by viewing energy as a wave. Blackbody experiment
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Results
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Energy is Quantized Planck found DE came in chunks with size hf
DE = nhf where n is an integer; h is Planck’s constant h = x J s these packets of hf are called quanta
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Einstein is next Electromagnetic radiation is quantized in particles called photons. Each photon has E = nhf (Plank) Wave equation: c=lf, f= c/l Combine this with Einstein’s E = mc2 You get the apparent mass of a photon. De Broglie thus assigned a wavelength to every mass, m = h / (lc)
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Spectrum Hydrogen spectrum
The range of frequencies present in light. White light has a continuous spectrum. Called an emission spectrum because these are the colors it gives off or emits. There are just a few discrete lines showing line spectrum Hydrogen spectrum 434 nm 656 nm 410 nm 486 nm
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Line spectra are unique to each element.
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What this means Only certain energies are allowed for the hydrogen atom. Can only give off certain energies. Use DE = hf = hc / l Energy in the in the atom is quantized.
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Niels Bohr Developed the quantum model of the hydrogen atom.
He said the atom was like a solar system. The electrons were attracted to the nucleus because of opposite charges. Didn’t fall in to the nucleus because it was moving around; centrifugal force Bohr found a flaw in Newtonian laws of mechanics (which govern large mass). They do not govern particles that have a small mass. Therefore, a new set of laws was developed.
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The Bohr Ring Atom He didn’t know why but only certain energies were allowed. He called these allowed energies energy levels. Putting Energy into the atom moved the electron away from the nucleus. From ground state to excited state. When it returns to ground state it gives off light of a certain energy.
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The Bohr Ring Atom n = 4 n = 3 n = 2 n = 1
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The Bohr Model Balmer created an equation that described the spectrum for Hydrogen. = RH ( ) R = 1.10 x 107 /m n = energy level used to calculate wavelength, frequency or energy of the light emitted in a transition from one energy level to another. 1 λ 1 nf 2 1 ni 2
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The Quantum Mechanical Model
The Bohr Model Only works for hydrogen atoms. Electrons don’t move in circles. The quantization of energy is right, but not because they are circling like planets. A totally new approach must be taken De Broglie said matter could be like a wave; specifically standing waves Similar to the vibrations of a stringed instrument. The Quantum Mechanical Model
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Schroedinger’s Equation
What’s possible? You can only have a standing wave if you have complete waves. There are only certain allowed waves. In the atom there are certain allowed waves given to each electron. 1925 Erwin Schroedinger described the wave function of the electron in 3-D; Solutions to the equation are called orbitals which describe the energy and motion of an eֿ around a nucleus. mathematical expression These are not Bohr orbits. Each solution is tied to a certain energy. These are the energy levels. Schroedinger’s Equation
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There is a limit to what we can know
We can’t know how the electron is moving or how it gets from one energy level to another. There is a limit to how well we can know both the position and the momentum of an object. The Heisenberg Uncertainty Principle.
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Probability Distance from nucleus
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Analogy If you have a regular camera and try to get pictures of a bullet that was fired A) You can take many pictures in fast succession…you get blurry images but a good sense of the speed of the bullet (don’t know the position but do know the motion of the bullet) B) You can take one clear picture…you get a clear idea of the position but the motion of the bullet is unclear (position known but motion unclear)
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Quantum Numbers There are many solutions to Schroedinger’s equation
Each solution can be described with four quantum numbers (n, l, ml and ms) that describe some aspect of the solution. Principal quantum number (n) size and energy of of an orbital. Has integer values >0 Represents the main shell
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Quantum numbers Angular momentum quantum number, l .
Describes the shape of the orbital. Sometimes called a subshell integer values from 0 to n-1 l = 0 is called s sharp l = 1 is called p principal l = 2 is called d diffuse l = 3 is called f fundamental
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S orbitals one s orbital for every energy level
Spherical shaped, only 1 orientation possible Each s orbital can hold 2 electrons Called the 1s, 2s, 3s, etc.. orbitals.
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P orbitals Start at the second energy level
3 different directions, x, y and z called -1,0 and 1 Each can hold 2 electrons Total of 6 electrons if all the p orbitals (x,y and z) are filled with 2 electrons each
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P Orbitals
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D orbitals Start at the third energy level n = 3; l=2
5 different orientations Each can hold Total of 10 electrons Orientations called -2,-1,0,1,2
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F orbitals Start at the fourth energy level Have seven
different orientations 2 electrons per shape for a total of 14 electrons, orientations called -3,-2,-1,0,1,2,3
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Quantum numbers Magnetic quantum number (m l)
integer values between - l and + l tells direction/orientation of each shape. Shape s (l=0) ml=0…1 orientation…called 0 Shape p (l=1) ml=-1,0,1…3 orientations…called x,y,z Shape d (l=2) ml=-2,-1,0,1,2…5 orientations… Shape f (l=3) ml=-3,-2,-1,0,1,2,3…7 orientations…
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Quantum numbers Electron spin quantum number (m s) Can have 2 values.
either +1/2 or -1/2 Either clockwise or counterclockwise He has 2 electrons in the first shell Electronic configuration of He: 1s2 The four quantum numbers of each of the 2 electrons are {n,l,ml,ms} {1,0,0,½}, {1,0,0,-½}
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Aufbau Principle Aufbau is German for building up.
As the protons are added one by one, the electrons fill up hydrogen-like orbitals. Fill up in order of energy levels.
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Increasing energy He with 2 electrons 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p
3d 4d 5d 7p 6d 4f 5f He with 2 electrons
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Details Valence electrons- the electrons in the outermost energy levels (not d). Core electrons- the inner electrons. Hund’s Rule- The lowest energy configuration for an atom is the one with the maximum number of unpaired electrons in the orbital. C 1s2 2s2 2p2
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Pauli Exclusion principle
no two electrons within a particular atom can have all four identical quantum numbers. this principle means that if two electrons occupy the same energy level, same orbital and same orientation they must have opposite spin. Eg, He: {1,0,0,½} and {1,0,0,-½}
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Fill from the bottom up following the arrows
2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 56 electrons
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Details Elements in the same column have the same electron configuration. Put in columns because of similar properties. Similar properties because of electron configuration. Noble gases have filled energy levels. Transition metals are filling the d orbitals
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Examples 1. Write the electronic configuration of the first 37 atoms H, He, Li, Be, B, C, N, O, F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, K, Ca, Sc, Ti, V, Cr, Mn Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Br, Kr, Rb 2. Write the condensed electronic configuration of the atoms from sodium to rubidium 3. Write the four quantum numbers for all of the electrons of the atom boron.
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Exceptions Ti = [Ar] 4s2 3d2 V = [Ar] 4s2 3d3 Cr = [Ar] 4s1 3d5
Mn = [Ar] 4s2 3d5 Half filled orbitals. Scientists aren’t sure of why it happens same for Cu [Ar] 4s1 3d10 Irregular pattern repeats for the other atoms in the same group as Cr and Cu
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Quantum Theory - summary
Quantum theory explains the wave-like nature of eֿ and the quantization of energy in the atom. Distinct energy levels can be identified by the principal quantum number, n The 2n² rule can still be applied. (max electrons per shell) Experimental data (ionization energies) show that eֿ in the same energy level do not possess the same energy. (i.e subshells exist) Evidence points to energy sublevel the number of different kinds of energy sublevel in principal level = n. The energy sublevels are designated in order of increasing energy, s, p, d, f.
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Some General Trends in the Periodic System
The last digit of the group number is indicative of the # of eֿ in highest energy level. (# valence electrons) The atoms of group 18 have completely filled s and p orbitals. The number of the period (row) is also the number of the highest energy levels occupied by electrons in the ground state. (row # is equal to the number of energy levels) The first, second, and third transition series elements correspond to 3d, 4d and 5d orbital being filled. Lanthanoids and actinoids are formed by filling the 4f and 5f orbitals. Atoms of the elements in group 1 and 17 have one more and one less electron than its nearest noble gas. These are extremely reactive.
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Periodic Table Alkali metals Noble Gases S S Halogens n=1
Alkaline Earth metals p p p n=2 Transition metals n=3 d n=4 3d n=5 4d n=6 5d n=7 6d Inner transition elements 4f 5f
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Periodicity in outer energy-level electron configuration
Transition elements – fill orbitals 3d, 4d , 5d , 6d Lanthanide Series – 4f orbitals Actinicide Series - 5f orbitals (inner transition elements) Group 1 elements → 1eֿ in outer s orbital - one more eֿ than noble gas proceeding it very reactive. metals (inert gases) Atoms in group 2 have 2eֿ in s orbital of highest energy level. S orbitals are filled. Group 17 elements → 2eֿ in s and 5eֿ in p at highest level one eֿ short of a noble gas configuration. → are very reactive Last digit of group # = # of eֿ in outer energy levels. Eg: Group 16 S, O, etc) have 6eֿ at outer level s²p4 . Group 18 have 8eֿ or completely filled s and p orbitals. → This makes them chemically inactive. s and p at highest energy level which matches row they belong to.
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Conclusion: 1. Similarities in chemistry and physics properties are paralleled by and reflect similarities in eֿ configurations. 2. High stability when s and p orbitals are filled. 3. Chemical behaviour is related to the eֿ configuration of the highest energy level.
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