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Orbitals and Quantum Numbers

Orbitals and Quantum Numbers. (. Drill. If the frequency of radiation is 4.68 x 10 -3 Hz. What is the wavelength of light in cm?. Objectives. iWBAT Distinguish between the 4 quantum numbers.

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Orbitals and Quantum Numbers

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  1. Orbitals and Quantum Numbers (

  2. Drill • If the frequency of radiation is 4.68 x 10 -3 Hz. What is the wavelength of light in cm?

  3. Objectives • iWBAT • Distinguish between the 4 quantum numbers. • describe the quantum numbers n, l, and ml used to define an orbital in an atom, and list the limitations placed on the values each may have. • Assign quantum numbers to specific electrons in atoms

  4. What is an orbital? • An orbital is an allowed energy state of an electron in the quantum-mechanical model of the atom • the term orbital is also used to describe the spatial distribution of the electron. • Defined by the values of 4 quantum numbers: n, l, and ml , ms

  5. 4 Quantum Numbers • Reminder: quantum numbers specify the properties of atomic orbitals and the properties of electrons in orbitals

  6. Principal Quantum Number “n” • The principal quantum number (n) indicates the main energy level occupied by the electron • n can have integral values of 1, 2, 3, etc.

  7. The Large Numbers Represent the Principal Quantum Numbers Principal Quantum Numbers http://www.angelo.edu/faculty/kboudrea/general/quantum_numbers/quantum_table1.gif

  8. http://library.thinkquest.org/15567/lessons/sublevels.jpg

  9. Azimuthal Quantum Number • The angular momentum (or azimuthal) quantum number (symbolized by “l “) indicates the shape of the orbital • “l “ can take on integral values from 0 to n -1 for each value of n L is Mistral font

  10. Which sublevel does each value of “l ” represent? • Value of l letter used 0 s 1 p 2 d 3 f

  11. http://chemwiki.ucdavis.edu/@api/deki/files/4826/=Single_electron_orbitals.jpghttp://chemwiki.ucdavis.edu/@api/deki/files/4826/=Single_electron_orbitals.jpg

  12. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/imgqua/hydco5.gifhttp://hyperphysics.phy-astr.gsu.edu/hbase/quantum/imgqua/hydco5.gif

  13. Magnetic Quantum Number • The magnetic quantum number ( ml ) describes the orientation of the orbital in space • It can take on values from “l to –l ” • For example: • If “l” is 2 then ml could be 2, 1, 0, -1, -2

  14. Electron Spin Quantum Number Electron Spin Quantum Number (ms ) • This number indicates the two fundamental spin states of an electron in an orbital • This quantum number can only have two possible values, + ½ or - ½

  15. http://www.brooklyn.cuny.edu/bc/ahp/LAD/C3/graphics/C3_quant_04.gifhttp://www.brooklyn.cuny.edu/bc/ahp/LAD/C3/graphics/C3_quant_04.gif http://quantumanthropology2.files.wordpress.com/2012/04/picture-paul-40.png

  16. Pauli Exclusion Principle • Pauli Exclusion Principle • states that no two electrons in an atom can have the same set of 4 quantum numbers n, l, ml, and ms

  17. http://www.chemistryland.com/CHM130W/10-ModernAtom/Spectra/PeriodicTableWithQuantumNumbers.jpghttp://www.chemistryland.com/CHM130W/10-ModernAtom/Spectra/PeriodicTableWithQuantumNumbers.jpg

  18. http://wps.prenhall.com/wps/media/objects/3081/3155040/blb0605/blb06t02.gifhttp://wps.prenhall.com/wps/media/objects/3081/3155040/blb0605/blb06t02.gif

  19. http://atomicstructureforelectrons.webs.com/quantum-number-pic.gifhttp://atomicstructureforelectrons.webs.com/quantum-number-pic.gif

  20. Practice Problem #1 • For n=4, what are the possible values of l ? • Answer on next slide.

  21. Answer • l = 0,1,2,3 • (what do these values correspond to?)

  22. Practice Problem #2 • For l =2, what are the possible values of ml ? • Answer on next slide.

  23. Answer • ml = 2,1,0,-1,-2 • (what do these values correspond to?)

  24. Can an e- be described by the following set of quantum numbers? n=2, l=1, ml=-1 All quantum numbers are allowed values

  25. Can an e- be described by the following set of quantum numbers? n=1, l=1, ml=+1 Not possible. The value of l must be less than the value of n.

  26. Can an e- be described by the following set of quantum numbers? n=7, l=3, ml=+3 All the quantum numbers are allowed values.

  27. Can an e- be described by the following set of quantum numbers? n=3, l=1, ml=-3 Not possible. The value of ml must be in the range -l to +l

  28. Can an e- be described by the following set of quantum numbers? n=2, l=1, ml=-2 n=3, l=2, ml=+2 n=4, l=3, ml=+3 n=5, l=2, ml=+3

  29. Replace the ? Mark with an appropriate quantum number. n=3, l=1, ml=? n=4, l=?, ml=-2 n=?, l=3, ml=?

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