IB Chemistry on Quantum Numbers, Electronic Configuration and De Broglie Wavelength

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 – particle
Orbit
Bohr Model equation:
• Angular momentum, L = nh/2π
L=
nh
2p
mvr =
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 electron
Electron – particle
Electron – Wave like nature
Orbit
Orbital
Bohr Model equation:
• Angular momentum, L = nh/2π
L=
nh
2p
mvr =
nh
2p
De Broglie wavelength equation • Electron -standing wave.
• E = mv2 and E = hf -> λ = h/mv
mv 2 = hf
mv 2 = h
v
l
Click here - electron wave
mv =
h
l
mv =
h
l

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 electron
Electron – particle
Electron – Wave like nature
Orbit
Orbital
De Broglie wavelength equation • Electron -standing wave.
• E = mv2 and E = hf -> λ = h/mv
Bohr Model equation:
• Angular momentum, L = nh/2π
L=
nh
2p
mvr =
nh
2p
mv 2 = hf
mv 2 = h
v
l
Click here - electron wave
mv =
h
l
mv =
h
l
Combine Bohr and De Broglie
mvr =
nh
2p
h
l
r=
nh
2p
nl = 2p r
nλ = 2πr
What does, nλ = 2πr means ?
•
•
•
•
Orbit/circumference - exact multiples of electron wavelength
Circumference of orbit- equal t0 1x wavelength, 2x wavelength,
3x wavelength or multiple of its wavelength, nλ
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, nλ
nλ = 2πr
n=1
1λ = 2πr1
ONE wavelength λ fits the 1st orbit
n=2
2λ = 2πr2
TWO wavelength λ fits the 2nd orbit
n=3
3λ = 2πr3
THREE wavelength λ 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, nλ
nλ = 2πr
n=1
1λ = 2πr1
ONE wavelength λ fits the 1st orbit
n=2
2λ = 2πr2
TWO wavelength λ fits the 2nd orbit
n=3
3λ = 2πr3
THREE wavelength λ fits the 3rd orbit
Standing wave around the circumference /circle
1λ
ONE wavelength λ fits the 1st orbit
1st Orbit
2λ
TWO wavelength λ fits the 2nd orbit
3λ
2nd Orbit
THREE wavelength λ fits the 3rd orbit
3rd 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, nλ
nλ = 2πr
n=1
1λ = 2πr1
ONE wavelength λ fits the 1st orbit
n=2
2λ = 2πr2
TWO wavelength λ fits the 2nd orbit
n=3
3λ = 2πr3
THREE wavelength λ fits the 3rd orbit
Standing wave around the circumference /circle
1λ
ONE wavelength λ fits the 1st orbit
1st Orbit
2λ
TWO wavelength λ fits the 2nd orbit
3λ
2nd Orbit
THREE wavelength λ fits the 3rd orbit
3rd Orbit
Relationship between wavelength and circumference
a o = 0.0529nm/Bohr radius
1λ
n=1
n=2
ONE wavelength λ
TWO wavelength λ
r n = n2 a 0
1λ1 = 2πr1
2λ
2λ2 = 2πr2
λ1 = 6.3 ao - 1st orbit
r n = n2 a 0
λ2= 12.6 ao - 2nd orbit
3λ
n=3
THREE wavelength λ
3λ3 = 2πr3
r n = n2 a 0
λ3 = 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, nλ
nλ = 2πr
ONE wavelength λ fits the 1st orbit
n=1
λ = 2πr1
n=2
2λ = 2πr2
TWO wavelength λ fits the 2nd orbit
n=3
3λ = 2πr3
THREE wavelength λ fits the 3rd orbit
Standing wave around the circumference /circle
λ
ONE wavelength λ fits the 1st orbit
1st Orbit
λ
TWO wavelength λ fits the 2nd orbit
λ
2nd Orbit
THREE wavelength λ fits the 3rd orbit
Click here to view video
Click here to view notes
Click here - electron wave simulation

9. Models for electronic orbitals
1913
1925
Bohr Model
De Broglie wavelength
Electron in fixed orbits
Electron form a standing wave
1927
Heisenberg Uncertainty principle

10. Models for electronic orbitals
1913
Bohr Model
1927
1925
De Broglie wavelength
Electron in fixed orbits
Electron form a standing wave
Heisenberg 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 space
ORBITAL is used to replace orbit
Δx = uncertainty in position
Δp = uncertainty in momentum/velocity
(ħ)= reduced plank constant

11. Models for electronic orbitals
1927
1913
1925
Bohr Model
De Broglie wavelength
Electron in fixed orbits
Heisenberg Uncertainty principle
•
Electron form a standing wave
•
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 don’t know its momentum, velocity
Δp 
electron
Δx
Big hole
electron
Δx 
electron
Probability/chance/likelyhood to find electron in space
Δx 
ORBITAL is used to replace orbit
Small hole
Reduce the hole smaller, x

Know precisely x, electron position

Uncertainty Δx is small ( Δx, Δp)

Δp is high so Δx Δp > h/2

Δp high – uncertainty in its velocity is high
Position of electron is unknown!
Δp = mass x velocity
Velocity is unknown
Δx = uncertainty in position
Δp = uncertainty in momentum/velocity
(ħ)= reduced plank constant
Probability/likelyhood to find an electron in space

12. Uncertainty for electron in space
1913
Bohr Model
1927
1925
De Broglie wavelength
Electron in fixed orbits
Electron form a standing wave
Heisenberg 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 don’t know its momentum, velocity
Probability/chance/likelyhood to find an electron
ORBITAL is used to replace orbit
Excellent video on uncertainty principle
Click here video on uncertainty principle
Video on uncertainty principle
Click here to view uncertainty principle
Δx = uncertainty in position
Δp = uncertainty in momentum/velocity
(ħ)= reduced plank constant

13. Schrödinger's wave function.
1927

14. Schrödinger's wave function.
1927
•
•
Schrödinger's wave function.
Mathematical description of electron given by wave function
Amplitude – probability of finding electron at any point in space/time
High probability
finding electron
electron density
•
•
•
Probability finding electron in space
Position electron unknown
Orbital ✔ NOT orbit ✗ used
is
•
•
•
Probability find electron distance from nucleus
Probability density used- Ψ2
Orbital NOT orbit is used
ORBITAL is used to replace orbit
ORBITAL• Mathematical description wavelike nature electron
• Wavefunction symbol – Ψ
• Probability finding electron in space

15. Schrödinger's wave function.
1927
•
•
Schrödinger's wave function.
Mathematical description of electron given by wave function
Amplitude – probability of finding electron at any point in space/time
High probability
finding electron
electron density
•
•
•
Bohr Model
✗
•
•
•
Probability finding electron in space
Position electron unknown
Orbital ✔ NOT orbit ✗ used
is
Schrödinger's wave function.
Probability find electron distance from nucleus
Probability density used- Ψ2
Orbital NOT orbit is used
✔
ORBITAL is used to replace orbit
ORBITAL• Mathematical description wavelike nature electron
• Wavefunction symbol – Ψ
• Probability finding electron in space
better description
electron behave
Click here to view simulation

16. Schrödinger's wave function.
1927
•
•
Schrödinger's wave function.
Mathematical description of electron given by wave function
Amplitude – probability of finding electron at any point in space/time
High probability
finding electron
electron density
•
•
•
Bohr Model
✗
•
•
•
Probability finding electron in space
Position electron unknown
Orbital ✔ NOT orbit ✗ used
is
Schrödinger's wave function.
Probability find electron distance from nucleus
Probability density used- Ψ2
Orbital NOT orbit is used
✔
ORBITAL is used to replace orbit
ORBITAL• Mathematical description wavelike nature electron
• Wavefunction symbol – Ψ
• Probability finding electron in space
better description
electron behave
Click here to view simulation
Click here to view simulation
Click here to view simulation

17. Four Quantum Numbers
•
•
•
1
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)
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)
1
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)
2
Angular Momentum Quantum Number (l): l = 0 to n-1.
• Orbital Shape
• Divides shells into subshells/sublevels.
• Letters (s, d, p, f)
s orbital
p orbital
d orbital
No 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)
1
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)
2
Angular Momentum Quantum Number (l): l = 0 to n-1.
• Orbital Shape
• Divides shells into subshells/sublevels.
• Letters (s, d, p, f)
s orbital
p orbital
d orbital
3
No TWO electron have same
4 quantum number
Magnetic Quantum Number (ml): ml = -l, 0, +l.
• Orientation orbital in space/direction
• mℓ range from −ℓ to ℓ,
• ℓ = 0 -> mℓ = 0
–> s sublevel -> 1 orbital
• ℓ = 1 -> mℓ = -1, 0, +1
-> p sublevel -> 3 diff p orbitals
• ℓ = 2 -> mℓ = -2, -1, 0, +1, +2 -> d sublevel -> 5 diff d orbitals
• (2l+ 1 ) quantum number for each ℓ 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)
1
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)
2
Angular Momentum Quantum Number (l): l = 0 to n-1.
• Orbital Shape
• Divides shells into subshells/sublevels.
• Letters (s, d, p, f)
s orbital
p orbital
3
4
No TWO electron have same
4 quantum number
Magnetic Quantum Number (ml): ml = -l, 0, +l.
• Orientation orbital in space/direction
• mℓ range from −ℓ to ℓ,
• ℓ = 0 -> mℓ = 0
–> s sublevel -> 1 orbital
• ℓ = 1 -> mℓ = -1, 0, +1
-> p sublevel -> 3 diff p orbitals
• ℓ = 2 -> mℓ = -2, -1, 0, +1, +2 -> d sublevel -> 5 diff d orbitals
• (2l+ 1 ) quantum number for each ℓ value
Spin 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/down
d 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)
1
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)
2
Angular Momentum Quantum Number (l): l = 0, ..., n-1.
• Orbital Shape
• Divides shells into subshells (sublevels)
• Letters (s,p,d,f)
• < less than n-1
Sublevels, 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)
1
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)
2
Angular Momentum Quantum Number (l): l = 0, ..., n-1.
• Orbital Shape
• Divides shells into subshells (sublevels)
• Letters (s,p,d,f)
• < less than n-1
Sublevels, l
Quantum number, n and l
l=1
2p sublevel
l=0
2s sublevel
n= 2
n= 1
1
Principal
Quantum #, n
(Size , energy)
l=0
2
1s sublevel
Angular momentum
quantum number, l
(Shape of orbital)
1
Principal Quantum
Number (n)
2
Angular 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)
1
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)
2
Angular Momentum Quantum Number (l): l = 0, ..., n-1.
• Orbital Shape
• Divides shells into subshells (sublevels)
• Letters (s,p,d,f)
• < less than n-1
Sublevels, l
Quantum number, n and l
l=1
2p sublevel
l=0
2s sublevel
n= 2
n= 1
1
Principal
Quantum #, n
(Size , energy)
l=0
2
1s sublevel
Angular momentum
quantum number, l
(Shape of orbital)
2p sublevel – contain 2p orbital
2nd energy level
Has TWO sublevels
2s sublevel – contain 2s orbital
1st energy level
Has ONE sublevel
1s sublevel – contain 1s orbital
1
Principal Quantum
Number (n)
2
Angular Momentum
Quantum Number (l)

24. Electronic Orbitals
n = 1, 2, 3,….
Allowed values
Energy Level
n= 3
n= 2
n= 1
1
Principal
Quantum #, n
(Size , energy)

25. Electronic Orbitals
n = 1, 2, 3,….
Allowed values
l = 0 to n-1
l=2
3d sublevel
l=1
3p sublevel
l=0
3s sublevel
l=1
2p sublevel
l=0
2s sublevel
l=0
1s sublevel
Energy Level
n= 3
n= 2
n= 1
1
Principal
Quantum #, n
(Size , energy)
2
Angular momentum
quantum number, l
(Shape of orbital)

26. Electronic Orbitals
n = 1, 2, 3,….
Allowed values
l = 0 to n-1
Allowed values
ml = -l, 0, +l- (2l+ 1 ) for each ℓ value
ml =+2
ml =+1
ml = 0
l=1
3px orbital
ml = 0
3s sublevel
3py orbital
3s orbital
ml =+1
l=0
3pz orbital
ml = 0
3p sublevel
3dxy orbital
ml =-1
l=1
3dxz orbital
ml =+1
n= 3
3dz2 orbital
ml =-2
3d sublevel
3dyz orbital
ml =-1
l=2
Energy Level
3dx2 – y2 orbital
2py orbital
ml = 0
2p sublevel
2pz orbital
ml =-1
n= 2
2px orbital
l=0
1
Principal
Quantum #, n
(Size , energy)
2
ml =0
2s orbital
l=0
n= 1
2s sublevel
1s sublevel
ml =0
1s orbital
Angular momentum
quantum number, l
(Shape of orbital)
3
Magnetic Quantum
Number (ml)
(Orientation orbital)

27. Electronic Orbitals
Simulation Electronic Orbitals
n = 1, 2, 3,….
Allowed values
l = 0 to n-1
Allowed values
ml = -l, 0, +l- (2l+ 1 ) for each ℓ value
ml =+2
ml =+1
ml = 0
l=1
3px orbital
ml = 0
3s sublevel
3py orbital
3s orbital
ml =+1
l=0
3pz orbital
ml = 0
3p sublevel
3dxy orbital
ml =-1
l=1
3dxz orbital
ml =+1
n= 3
3dz2 orbital
ml =-2
3d sublevel
3dyz orbital
ml =-1
l=2
Energy Level
3dx2 – y2 orbital
2py orbital
ml = 0
2p sublevel
2pz orbital
ml =-1
n= 2
2px orbital
l=0
1
Principal
Quantum #, n
(Size , energy)
2
2s sublevel
ml =0
1s sublevel
ml =0
Click here to view simulation
2s orbital
l=0
n= 1
Click here to view simulation
1s orbital
Angular momentum
quantum number, l
(Shape of orbital)
3
Magnetic Quantum
Number (ml)
(Orientation orbital)
Click here to view simulation

28. Quantum Numbers and Electronic Orbitals
Energy Level
n= 3
n= 2
n= 1

29. Quantum Numbers and Electronic Orbitals
Energy Level
l=2
3d sublevel
l=1
3p sublevel
l=0
3s sublevel
l=1
2p sublevel
l=0
2s sublevel
l=0
1s sublevel
n= 3
n= 2
n= 1

30. Quantum Numbers and Electronic Orbitals
ml =+2
Energy Level
3dx2 – y2orbital
ml =+1
3dz2 orbital
3dxz orbital
ml =-2
3d sublevel
ml = 0
ml =-1
l=2
3dyz orbital
3dxy orbital
n= 3
ml =+1
l=1
3s sublevel
2p sublevel
n= 2
3pz orbital
3px orbital
ml = 0
3s orbital
ml =+1
l=0
3p sublevel
ml = 0
ml =-1
l=1
3py orbital
2py orbital
ml = 0
2pz orbital
ml =-1
2px orbital
l=0
n= 1
2s sublevel
ml =0
2s orbital
l=0
1s sublevel
ml =0
1s orbital

31. Quantum Numbers and Electronic Orbitals
ml =+2
3dx2 – y2orbital
Simulation Electronic Orbitals
Energy Level
ml =+1
3d sublevel
ml = 0
3dz2 orbital
ml =-1
l=2
3dyz orbital
3dxz orbital
Click here to view simulation
n= 3
ml =-2
3dxy orbital
ml =+1
3p sublevel
ml = 0
3pz orbital
ml =-1
l=1
3py orbital
3px orbital
Click here to view simulation
l=0
2p sublevel
n= 2
ml = 0
3s orbital
ml =+1
l=1
3s sublevel
2py orbital
ml = 0
2pz orbital
ml =-1
2px orbital
l=0
n= 1
2s sublevel
ml =0
2s orbital
l=0
1s sublevel
ml =0
1s orbital
Click here to view simulation

32. Concept Map
Quantum number
No TWO electron have same
4 quantum number
Quantum number = genetic code for electron
Electron has special number codes

33. Concept Map
No TWO electron have same
4 quantum number
Quantum number
Quantum number = genetic code for electron
What are these 4 numbers?
(1, 0, 0, +1/2) 0r (3, 1, 1, +1/2)
4 numbers
n
l
Size/distance
Shape
Number + letter
ml
Orientation
ms
Electron spin
Electron has special number codes

34. Concept Map
No TWO electron have same
4 quantum number
Quantum number
Quantum number = genetic code for electron
What are these 4 numbers?
(1, 0, 0, +1/2) 0r (3, 1, 1, +1/2)
4 numbers
n
l
Size/distance
Shape
ml
Orientation
Number + letter
1
Electron with quantum number given below
(n,l,ml,,ms) – (1, 0, 0, +1/2)
1s orbital
ms
Electron spin
Electron has special number codes

35. Concept Map
No TWO electron have same
4 quantum number
Quantum number
Quantum number = genetic code for electron
What are these 4 numbers?
(1, 0, 0, +1/2) 0r (3, 1, 1, +1/2)
4 numbers
n
l
Size/distance
Shape
ml
Orientation
Number + letter
1
Electron 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 orbital
ms
Electron spin
Electron has special number codes

36. Concept Map
No TWO electron have same
4 quantum number
Quantum number
Quantum number = genetic code for electron
What are these 4 numbers?
(1, 0, 0, +1/2) 0r (3, 1, 1, +1/2)
4 numbers
n
l
Size/distance
Shape
ml
Orientation
ms
Electron has special number codes
Electron spin
Number + letter
1
Electron with quantum number given below
(n,l,ml,,ms) – (1, 0, 0, +1/2)
(n,l,ml,,ms) – (3, 1, 1, +1/2)
2
1s orbital
3py orbital
What values of l, ml, allow for n = 3? How many orbitals exists for n=3?
Video on Quantum numbers
For n=3 -> l = n -1 =2 -> ml = -l, 0, +l -> -2, -1, 0, +1, +2
• mℓ range from −ℓ to ℓ,
• ℓ = 0 -> mℓ = 0
–> s sublevel -> 1 orbital
• ℓ = 1 -> mℓ = -1, 0, +1
-> p sublevel -> 3 diff p orbitals
• ℓ = 2 -> mℓ = -2, -1, 0, +1, +2 -> d sublevel -> 5 diff d orbitals
• (2l+ 1 ) quantum number for each ℓ value
Answer = nine ml values – 9 orbitals/ total # orbitals = n 2
Click here video on quantum number
Click 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