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

1. How electrons move?
•
•
Quantum Model
•Electron as standing wave around nucleus
•Electron NOT in fixed position
•ORBITAL – probability/chance finding electron
Bohr Model
Electron as particle
Electron orbit in FIXED radius from nucleus
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
2
mvr 
nh
2
mv 2 = hf
mv 2  h
Click here - electron wave
v

mv 
h

mv 
Combine Bohr and De Broglie
mvr 
nh
2
h

r
nh
2
n  2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
h


2. 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

3. 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

4. Models for electronic orbitals
1927
1925
1913
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
Δx 
Probability/chance/likelyhood to find electron in space
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

5. Uncertainty for electron in space
Bohr Model
Electron in fixed orbits
1927
1925
1913
De Broglie wavelength
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

6. 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
✗ is used
Orbital ✔ NOT orbit
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

7. 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', 'm l' 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
No TWO electron have same
4 quantum number
3
4
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

8. 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', 'm l' 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)

9. 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
l=2
3d sublevel
ml = 0
Energy Level
ml =-1
ml =-2
ml =+1
n= 3
l=1
3p sublevel
ml = 0
ml =-1
l=0
3s sublevel
ml = 0
ml =+1
l=1
ml = 0
2p sublevel
ml =-1
n= 2
l=0
1
Principal
Quantum #, n
(Size , energy)
2
ml =0
l=0
n= 1
2s sublevel
1s sublevel
ml =0
Angular momentum
quantum number, l
(Shape of orbital)
3
3dx2 – y2 orbital
3dyz orbital
3dz2 orbital
3dxz orbital
3dxy orbital
Click here to view simulation
3pz orbital
3py orbital
3px orbital
3s orbital
2py orbital
2pz orbital
Click here to view simulation
2px orbital
2s orbital
1s orbital
Magnetic Quantum
Number (ml)
(Orientation orbital)
Click here to view simulation

10. 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

11. 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) or (3, 1, 1, +1/2)
4 numbers
n
l
ml
ms
Size/distance
Shape
Orientation
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