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Quantum Numbers

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Quantum Numbers. How does a letter get to you? 5501 Haltom Rd Haltom City, TX 76137. How does a letter get to you? 5501 Haltom Rd Haltom City, TX 76137. Very general – includes many cities. How does a letter get to you? 5501 Haltom Rd Haltom City, TX 76137.

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Presentation Transcript
slide2

How does a letter get to you?

5501 Haltom Rd

Haltom City, TX 76137

slide3

How does a letter get to you?

5501 Haltom Rd

Haltom City, TX 76137

Very general – includes many cities

slide4

How does a letter get to you?

5501 Haltom Rd

Haltom City, TX 76137

Very general – includes many cities

Still general – includes a handful of cities

slide5

How does a letter get to you?

5501 Haltom Rd

Haltom City, TX 76137

Very general – includes many cities

Still general – includes a handful of cities

Specific, but includes many places

slide6

How does a letter get to you?

5501 Haltom Rd

Haltom City, TX 76137

Very specific – specifies only 1 place

Very general – includes many cities

Still general – includes a handful of cities

Specific, but includes many places

slide7

Quantum numbers are mathematical “addresses” of electrons for an atom – no two electrons can have the same exact address

slide8

Summary

Notes

slide9

Quantum numbers are mathematical “addresses” of electrons for an atom – no two electrons can have the same exact address

(n, l, ml, ms) => title

slide10

Notes

Summary

  • n = principle quantum number
    • energy level
    • relates to size
    • possible values are all positive integers (1 to ∞)
    • n = 1, 2, 3, 4, 5, 6, 7
    • (seven periods on the periodic table)
slide11

Notes

Summary

  • l = azimuthal quantum number
    • sublevel
    • relates to shape
    • possible values are 0 to n-1 (currently 0-3)
    • s = 0
    • p = 1
    • d = 2
    • f = 3
slide12

ml = magnetic quantum number

    • orbitals
    • possible values are integers from –l to l
    • if l = 0 , then s = 0
    • if l = 1, then p = -1, 0, 1
    • if l = 2, then d = -2, -1, 0, 1, 2
    • if l = 3, then f = -3, -2, -1, 0, 1, 2, 3

Notes

Summary

slide13

Notes

Summary

  • ms = spin quantum number
    • spin of the electron
    • possible values are ½ and -½
    • = ½
    • = -½
slide14

example – Ti (22 electrons)

orbital notation

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

slide15

example – Ti (22 electrons)

orbital notation

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

1st arrow (1, 0, 0, ½)

slide16

example – Ti (22 electrons)

orbital notation

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

1st arrow (1, 0, 0, ½)

2nd arrow (1, 0, 0, -½)

slide17

example – Ti (22 electrons)

orbital notation

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

1st arrow (1, 0, 0, ½)

2nd arrow (1, 0, 0, -½)

Can be combined into (1, 0, 0, ±½)

slide18

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

3rd and 4th arrows = (2, 0, 0, ±½)

slide19

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

3rd and 4th arrows = (2, 0, 0, ±½)

for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½)

slide20

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

3rd and 4th arrows = (2, 0, 0, ±½)

for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½)

for 3s: (3, 0, 0, ±½)

slide21

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

3rd and 4th arrows = (2, 0, 0, ±½)

for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½)

for 3s: (3, 0, 0, ±½)

for 3p: (3, 1, -1, ±½) and (3, 1, 0, ±½) and (3, 1, 1, ±½)

slide22

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

3rd and 4th arrows = (2, 0, 0, ±½)

for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½)

for 3s: (3, 0, 0, ±½)

for 3p: (3, 1, -1, ±½) and (3, 1, 0, ±½) and (3, 1, 1, ±½)

for 4s: (4, 0, 0, ±½)

slide23

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

  • 1s 2s 2p 3s 3p 4s 3d
  • 3rd and 4th arrows = (2, 0, 0, ±½)
  • for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½)
  • for 3s: (3, 0, 0, ±½)
  • for 3p: (3, 1, -1, ±½) and (3, 1, 0, ±½) and (3, 1, 1, ±½)
  • for 4s: (4, 0, 0, ±½)
  • for 3d: (3, 2, -2, ½) and (3, 2, -1, ½)
      • notice -- no more arrows
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