1.Tutorial on Quantum Number, Electronic Configuration and De Broglie Wavelength.Prepared by Lawrence Kok http://lawrencekok.blogspot.com

2. How electrons move? Bohr Model Electron as particle Electron orbit in FIXED radius from nucleus Electron particleOrbitBohr Model equation: Angular momentum, L = nh/2L=nh 2pmvr =nh 2p 3. How electrons move? Bohr Model Electron as particle Electron orbit in FIXED radius from nucleus Quantum Model Electron as standing wave around nucleus Electron NOT in fixed position ORBITAL probability/chance finding electronElectron particleElectron Wave like natureOrbitOrbitalBohr Model equation: Angular momentum, L = nh/2L=nh 2pmvr =nh 2pDe Broglie wavelength equation Electron -standing wave. E = mv2 and E = hf -> = h/mvmv 2 = hfmv 2 = hvlClick here - electron wavemv =hlmv =hl 4. How electrons move? Bohr Model Electron as particle Electron orbit in FIXED radius from nucleus Quantum Model Electron as standing wave around nucleus Electron NOT in fixed position ORBITAL probability/chance finding electronElectron particleElectron Wave like natureOrbitOrbitalDe Broglie wavelength equation Electron -standing wave. E = mv2 and E = hf -> = h/mvBohr Model equation: Angular momentum, L = nh/2L=nh 2pmvr =nh 2pmv 2 = hfmv 2 = hvlClick here - electron wavemv =hlmv =hlCombine Bohr and De Brogliemvr =nh 2phlr=nh 2pnl = 2p r n = 2rWhat does, n = 2r means ? Orbit/circumference - exact multiples of electron wavelength Circumference of orbit- equal t0 1x wavelength, 2x wavelength, 3x wavelength or multiple of its wavelength, n Electron as standing wave around the nucleus Wavelength fits around the circumference of the orbit 5. Electron Wavelength around orbit Electron acts as standing wave surrounding the nucleus Wavelength fits around the circumference of the orbit Orbit/circumference - exact multiples of electron wavelength Circumference of orbit- equal the wavelength, 2x wavelength, 3x wavelength or multiple of its wavelength, nn = 2r n=11 = 2r1ONE wavelength fits the 1st orbitn=22 = 2r2TWO wavelength fits the 2nd orbitn=33 = 2r3THREE wavelength fits the 3rd orbit 6. Electron Wavelength around orbit Electron acts as standing wave surrounding the nucleus Wavelength fits around the circumference of the orbit Orbit/circumference - exact multiples of electron wavelength Circumference of orbit- equal the wavelength, 2x wavelength, 3x wavelength or multiple of its wavelength, nn = 2r n=11 = 2r1ONE wavelength fits the 1st orbitn=22 = 2r2TWO wavelength fits the 2nd orbitn=33 = 2r3THREE wavelength fits the 3rd orbitStanding wave around the circumference /circle1 ONE wavelength fits the 1st orbit 1st Orbit2 TWO wavelength fits the 2nd orbit3 2nd Orbit THREE wavelength fits the 3rd orbit3rd Orbit 7. Electron Wavelength around orbit Electron acts as standing wave surrounding the nucleus Wavelength fits around the circumference of the orbit Orbit/circumference - exact multiples of electron wavelength Circumference of orbit- equal the wavelength, 2x wavelength, 3x wavelength or multiple of its wavelength, nn = 2r n=11 = 2r1ONE wavelength fits the 1st orbitn=22 = 2r2TWO wavelength fits the 2nd orbitn=33 = 2r3THREE wavelength fits the 3rd orbitStanding wave around the circumference /circle1 ONE wavelength fits the 1st orbit 1st Orbit2 TWO wavelength fits the 2nd orbit3 2nd Orbit THREE wavelength fits the 3rd orbit3rd OrbitRelationship between wavelength and circumferencea o = 0.0529nm/Bohr radius1n=1n=2ONE wavelength TWO wavelength r n = n2 a 011 = 2r1 222 = 2r21 = 6.3 ao - 1st orbitr n = n2 a 02= 12.6 ao - 2nd orbit3n=3THREE wavelength 33 = 2r3r n = n2 a 03 = 18.9 ao - 3rd orbit 8. Electron Wavelength around orbit Electron acts as standing wave around the nucleus Wavelength fits around circumference of orbit Orbit/circumference - exact multiples of electron wavelength Circumference of orbit- equal t0 1x wavelength, 2x wavelength, 3x wavelength or multiple of its wavelength, nn = 2r ONE wavelength fits the 1st orbitn=1 = 2r1n=22 = 2r2TWO wavelength fits the 2nd orbitn=33 = 2r3THREE wavelength fits the 3rd orbitStanding wave around the circumference /circle ONE wavelength fits the 1st orbit 1st Orbit TWO wavelength fits the 2nd orbit 2nd Orbit THREE wavelength fits the 3rd orbitClick here to view videoClick here to view notesClick here - electron wave simulation 9. Models for electronic orbitals 19131925Bohr ModelDe Broglie wavelengthElectron in fixed orbitsElectron form a standing wave1927Heisenberg Uncertainty principle 10. Models for electronic orbitals 1913Bohr Model19271925De Broglie wavelengthElectron in fixed orbitsElectron form a standing waveHeisenberg Uncertainty principle Impossible to determine both the position and velocity of electron at the same time. Applies to electron, small and moving fast..Probability/chance/likelyhood to find electron in spaceORBITAL is used to replace orbitx = uncertainty in position p = uncertainty in momentum/velocity ()= reduced plank constant 11. Models for electronic orbitals 192719131925Bohr ModelDe Broglie wavelengthElectron in fixed orbitsHeisenberg Uncertainty principle Electron form a standing waveImpossible to determine both the position and velocity of electron at the same time. Applies to electron, small and moving fast..If we know position, x very precisely we dont know its momentum, velocity p electronxBig holeelectronx electronProbability/chance/likelyhood to find electron in spacex ORBITAL is used to replace orbitSmall holeReduce the hole smaller, x Know precisely x, electron position Uncertainty x is small ( x, p) p is high so x p > h/2 p high uncertainty in its velocity is highPosition of electron is unknown!p = mass x velocity Velocity is unknownx = uncertainty in position p = uncertainty in momentum/velocity ()= reduced plank constantProbability/likelyhood to find an electron in space 12. Uncertainty for electron in space 1913Bohr Model19271925De Broglie wavelengthElectron in fixed orbitsElectron form a standing waveHeisenberg Uncertainty principle Impossible to determine both the position and velocity of electron at the same time. Applies to electron, small and moving fast..If we know position, x very precisely we dont know its momentum, velocity Probability/chance/likelyhood to find an electronORBITAL is used to replace orbitExcellent video on uncertainty principleClick here video on uncertainty principleVideo on uncertainty principleClick here to view uncertainty principlex = uncertainty in position p = uncertainty in momentum/velocity ()= reduced plank constant 13. Schrdinger's wave function.1927 14. Schrdinger's wave function.1927 Schrdinger's wave function. Mathematical description of electron given by wave function Amplitude probability of finding electron at any point in space/timeHigh probability finding electronelectron density Probability finding electron in space Position electron unknown Orbital NOT orbit used is Probability find electron distance from nucleus Probability density used- 2 Orbital NOT orbit is usedORBITAL is used to replace orbitORBITAL Mathematical description wavelike nature electron Wavefunction symbol Probability finding electron in space 15. Schrdinger's wave function.1927 Schrdinger's wave function. Mathematical description of electron given by wave function Amplitude probability of finding electron at any point in space/timeHigh probability finding electronelectron density Bohr Model Probability finding electron in space Position electron unknown Orbital NOT orbit used isSchrdinger's wave function.Probability find electron distance from nucleus Probability density used- 2 Orbital NOT orbit is used ORBITAL is used to replace orbitORBITAL Mathematical description wavelike nature electron Wavefunction symbol Probability finding electron in spacebetter description electron behave Click here to view simulation 16. Schrdinger's wave function.1927 Schrdinger's wave function. Mathematical description of electron given by wave function Amplitude probability of finding electron at any point in space/timeHigh probability finding electronelectron density Bohr Model Probability finding electron in space Position electron unknown Orbital NOT orbit used isSchrdinger's wave function.Probability find electron distance from nucleus Probability density used- 2 Orbital NOT orbit is used ORBITAL is used to replace orbitORBITAL Mathematical description wavelike nature electron Wavefunction symbol Probability finding electron in spacebetter description electron behave Click here to view simulationClick here to view simulationClick here to view simulation 17. Four Quantum Numbers 1Electrons arrange in specific energy level and sublevels Orbitals of electrons in atom differ in size, shape and orientation. Allow states call orbitals, given by four quantum number 'n', 'l', 'ml' and ms - (n, l, ml, ms)Principal Quantum Number (n): n = 1, 2, 3,.. Energy of electron and size of orbital/shell Distance from nucleus, (higher n higher energy) Larger n - farther e from nucleus larger size orbital n=1, 1stprincipal shell ( innermost/ground shell state)No TWO electron have same 4 quantum number 18. Four Quantum Numbers Electrons arrange in specific energy level and sublevels Orbitals of electrons in atom differ in size, shape and orientation. Allow states call orbitals, given by four quantum number 'n', 'l', 'ml' and ms - (n, l, ml, ms)1Principal Quantum Number (n): n = 1, 2, 3,.. Energy of electron and size of orbital/shell Distance from nucleus, (higher n higher energy) Larger n - farther e from nucleus larger size orbital n=1, 1stprincipal shell ( innermost/ground shell state)2Angular Momentum Quantum Number (l): l = 0 to n-1. Orbital Shape Divides shells into subshells/sublevels. Letters (s, d, p, f) s orbitalp orbitald orbitalNo TWO electron have same 4 quantum number 19. Four Quantum Numbers Electrons arrange in specific energy level and sublevels Orbitals of electrons in atom differ in size, shape and orientation. Allow states call orbitals, given by four quantum number 'n', 'l', 'ml' and ms - (n, l, ml, ms)1Principal Quantum Number (n): n = 1, 2, 3,.. Energy of electron and size of orbital/shell Distance from nucleus, (higher n higher energy) Larger n - farther e from nucleus larger size orbital n=1, 1stprincipal shell ( innermost/ground shell state)2Angular Momentum Quantum Number (l): l = 0 to n-1. Orbital Shape Divides shells into subshells/sublevels. Letters (s, d, p, f) s orbitalp orbitald orbital3No TWO electron have same 4 quantum numberMagnetic Quantum Number (ml): ml = -l, 0, +l. Orientation orbital in space/direction m range from to , = 0 -> m = 0 > s sublevel -> 1 orbital = 1 -> m = -1, 0, +1 -> p sublevel -> 3 diff p orbitals = 2 -> m = -2, -1, 0, +1, +2 -> d sublevel -> 5 diff d orbitals (2l+ 1 ) quantum number for each value 20. Four Quantum Numbers Electrons arrange in specific energy level and sublevels Orbitals of electrons in atom differ in size, shape and orientation. Allow states call orbitals, given by four quantum number 'n', 'l', 'ml' and ms - (n, l, ml, ms)1Principal Quantum Number (n): n = 1, 2, 3,.. Energy of electron and size of orbital/shell Distance from nucleus, (higher n higher energy) Larger n - farther e from nucleus larger size orbital n=1, 1stprincipal shell ( innermost/ground shell state)2Angular Momentum Quantum Number (l): l = 0 to n-1. Orbital Shape Divides shells into subshells/sublevels. Letters (s, d, p, f) s orbitalp orbital34No TWO electron have same 4 quantum numberMagnetic Quantum Number (ml): ml = -l, 0, +l. Orientation orbital in space/direction m range from to , = 0 -> m = 0 > s sublevel -> 1 orbital = 1 -> m = -1, 0, +1 -> p sublevel -> 3 diff p orbitals = 2 -> m = -2, -1, 0, +1, +2 -> d sublevel -> 5 diff d orbitals (2l+ 1 ) quantum number for each valueSpin Quantum Number (ms): ms = +1/2 or -1/2 Each orbital 2 electrons, spin up/down Pair electron spin opposite direction One spin up, ms = +1/2 One spin down, ms = -1/2 No net spin/cancel out each other diamagnetic electron writing electron spin electron spin up/downd orbital 21. Principal and Angular Momentum Quantum numbers Electrons arrange in specific energy level and sublevels Orbitals of electrons in atom differ in size, shape and orientation. Allow states call orbitals, given by four quantum number 'n', 'l', 'ml' and ms - (n, l, ml, ms)1Principal Quantum Number (n): n = 1, 2, 3, , Energy of electron and size of orbital /shell Distance from nucleus, (higher n higher energy) Larger n - farther e from nucleus larger size orbital n=1, 1stprincipal shell ( innermost/ground shell state)2Angular Momentum Quantum Number (l): l = 0, ..., n-1. Orbital Shape Divides shells into subshells (sublevels) Letters (s,p,d,f) < less than n-1Sublevels, l 22. Principal and Angular Momentum Quantum numbers Electrons arrange in specific energy level and sublevels Orbitals of electrons in atom differ in size, shape and orientation. Allow states call orbitals, given by four quantum number 'n', 'l', 'ml' and ms - (n, l, ml, ms)1Principal Quantum Number (n): n = 1, 2, 3, , Energy of electron and size of orbital /shell Distance from nucleus, (higher n higher energy) Larger n - farther e from nucleus larger size orbital n=1, 1stprincipal shell ( innermost/ground shell state)2Angular Momentum Quantum Number (l): l = 0, ..., n-1. Orbital Shape Divides shells into subshells (sublevels) Letters (s,p,d,f) < less than n-1Sublevels, lQuantum number, n and ll=12p sublevell=02s subleveln= 2n= 1 1Principal Quantum #, n (Size , energy)l=0 21s sublevelAngular momentum quantum number, l (Shape of orbital)1Principal Quantum Number (n)2Angular Momentum Quantum Number (l) 23. Principal and Angular Momentum Quantum numbers Electrons arrange in specific energy level and sublevels Orbitals of electrons in atom differ in size, shape and orientation. Allow states call orbitals, given by four quantum number 'n', 'l', 'ml' and ms - (n, l, ml, ms)1Principal Quantum Number (n): n = 1, 2, 3, , Energy of electron and size of orbital /shell Distance from nucleus, (higher n higher energy) Larger n - farther e from nucleus larger size orbital n=1, 1stprincipal shell ( innermost/ground shell state)2Angular Momentum Quantum Number (l): l = 0, ..., n-1. Orbital Shape Divides shells into subshells (sublevels) Letters (s,p,d,f) < less than n-1Sublevels, lQuantum number, n and ll=12p sublevell=02s subleveln= 2n= 1 1Principal Quantum #, n (Size , energy)l=0 21s sublevelAngular momentum quantum number, l (Shape of orbital) 2p sublevel contain 2p orbital2nd energy levelHas TWO sublevels 2s sublevel contain 2s orbital1st energy levelHas ONE sublevel1s sublevel contain 1s orbital1Principal Quantum Number (n)2Angular Momentum Quantum Number (l) 24. Electronic Orbitals n = 1, 2, 3,.Allowed valuesEnergy Leveln= 3n= 2n= 11Principal Quantum #, n (Size , energy) 25. Electronic Orbitals n = 1, 2, 3,.Allowed valuesl = 0 to n-1l=23d sublevell=13p sublevell=03s sublevell=12p sublevell=02s sublevell=01s sublevelEnergy Leveln= 3n= 2n= 11Principal Quantum #, n (Size , energy)2Angular momentum quantum number, l (Shape of orbital) 26. Electronic Orbitals n = 1, 2, 3,.Allowed valuesl = 0 to n-1Allowed valuesml = -l, 0, +l- (2l+ 1 ) for each value ml =+2 ml =+1 ml = 0l=13px orbitalml = 03s sublevel3py orbital3s orbitalml =+1l=03pz orbitalml = 03p sublevel3dxy orbitalml =-1l=13dxz orbitalml =+1 n= 33dz2 orbitalml =-23d sublevel3dyz orbitalml =-1l=2 Energy Level3dx2 y2 orbital2py orbitalml = 02p sublevel2pz orbitalml =-1n= 22px orbitall=01Principal Quantum #, n (Size , energy)2ml =02s orbitall=0n= 12s sublevel1s sublevelml =01s orbitalAngular momentum quantum number, l (Shape of orbital)3Magnetic Quantum Number (ml) (Orientation orbital) 27. Electronic Orbitals Simulation Electronic Orbitals n = 1, 2, 3,.Allowed valuesl = 0 to n-1Allowed valuesml = -l, 0, +l- (2l+ 1 ) for each value ml =+2 ml =+1 ml = 0l=13px orbitalml = 03s sublevel3py orbital3s orbitalml =+1l=03pz orbitalml = 03p sublevel3dxy orbitalml =-1l=13dxz orbitalml =+1 n= 33dz2 orbitalml =-23d sublevel3dyz orbitalml =-1l=2 Energy Level3dx2 y2 orbital2py orbitalml = 02p sublevel2pz orbitalml =-1n= 22px orbitall=01Principal Quantum #, n (Size , energy)22s sublevelml =01s sublevelml =0Click here to view simulation2s orbitall=0n= 1Click here to view simulation1s orbitalAngular momentum quantum number, l (Shape of orbital)3Magnetic Quantum Number (ml) (Orientation orbital)Click here to view simulation 28. Quantum Numbers and Electronic OrbitalsEnergy Leveln= 3n= 2n= 1 29. Quantum Numbers and Electronic OrbitalsEnergy Levell=23d sublevell=13p sublevell=03s sublevell=12p sublevell=02s sublevell=01s subleveln= 3n= 2n= 1 30. Quantum Numbers and Electronic Orbitals ml =+2Energy Level3dx2 y2orbitalml =+13dz2 orbital3dxz orbitalml =-23d sublevelml = 0ml =-1l=23dyz orbital3dxy orbitaln= 3ml =+1l=13s sublevel2p subleveln= 23pz orbital 3px orbitalml = 03s orbitalml =+1l=03p sublevelml = 0 ml =-1l=13py orbital2py orbitalml = 02pz orbitalml =-12px orbitall=0n= 12s sublevelml =02s orbitall=01s sublevelml =01s orbital 31. Quantum Numbers and Electronic Orbitals ml =+23dx2 y2orbitalSimulation Electronic Orbitals Energy Levelml =+13d sublevelml = 03dz2 orbitalml =-1l=23dyz orbital3dxz orbital Click here to view simulationn= 3 ml =-23dxy orbitalml =+1 3p sublevelml = 03pz orbitalml =-1l=13py orbital3px orbitalClick here to view simulation l=02p subleveln= 2ml = 03s orbitalml =+1 l=13s sublevel2py orbitalml = 02pz orbitalml =-12px orbitall=0n= 12s sublevelml =02s orbitall=01s sublevelml =01s orbitalClick here to view simulation 32. Concept MapQuantum numberNo TWO electron have same 4 quantum numberQuantum number = genetic code for electronElectron has special number codes 33. Concept MapNo TWO electron have same 4 quantum numberQuantum numberQuantum number = genetic code for electronWhat are these 4 numbers? (1, 0, 0, +1/2) 0r (3, 1, 1, +1/2) 4 numbersnlSize/distanceShapeNumber + lettermlOrientationmsElectron spinElectron has special number codes 34. Concept MapNo TWO electron have same 4 quantum numberQuantum numberQuantum number = genetic code for electronWhat are these 4 numbers? (1, 0, 0, +1/2) 0r (3, 1, 1, +1/2) 4 numbersnlSize/distanceShapemlOrientationNumber + letter1Electron with quantum number given below(n,l,ml,,ms) (1, 0, 0, +1/2)1s orbitalmsElectron spinElectron has special number codes 35. Concept MapNo TWO electron have same 4 quantum numberQuantum numberQuantum number = genetic code for electronWhat are these 4 numbers? (1, 0, 0, +1/2) 0r (3, 1, 1, +1/2) 4 numbersnlSize/distanceShapemlOrientationNumber + letter1Electron with quantum number given below(n,l,ml,,ms) (1, 0, 0, +1/2)1s orbital(n,l,ml,,ms) (3, 1, 1, +1/2)3py orbitalmsElectron spinElectron has special number codes 36. Concept MapNo TWO electron have same 4 quantum numberQuantum numberQuantum number = genetic code for electronWhat are these 4 numbers? (1, 0, 0, +1/2) 0r (3, 1, 1, +1/2) 4 numbersnlSize/distanceShapemlOrientationmsElectron has special number codesElectron spinNumber + letter1Electron with quantum number given below(n,l,ml,,ms) (1, 0, 0, +1/2)(n,l,ml,,ms) (3, 1, 1, +1/2)21s orbital3py orbitalWhat values of l, ml, allow for n = 3? How many orbitals exists for n=3?Video on Quantum numbersFor n=3 -> l = n -1 =2 -> ml = -l, 0, +l -> -2, -1, 0, +1, +2 m range from to , = 0 -> m = 0 > s sublevel -> 1 orbital = 1 -> m = -1, 0, +1 -> p sublevel -> 3 diff p orbitals = 2 -> m = -2, -1, 0, +1, +2 -> d sublevel -> 5 diff d orbitals (2l+ 1 ) quantum number for each value Answer = nine ml values 9 orbitals/ total # orbitals = n 2 Click here video on quantum numberClick here video on quantum number 37. Acknowledgements Thanks to source of pictures and video used in this presentation Thanks to Creative Commons for excellent contribution on licenses http://creativecommons.org/licenses/Prepared by Lawrence Kok Check out more video tutorials from my site and hope you enjoy this tutorial http://lawrencekok.blogspot.com