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IB Chemistry on Quantum Numbers, Electronic Configuration and De Broglie Wavelength
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How electrons move?
Bohr Model • Electron as particle • Electron orbit in FIXED radius from nucleus
Bohr Model equation: •Angular momentum, L = nh/2π
Electron – particle
De Broglie wavelength equation: •Electron -standing wave. •E = mv2 and E = hf -> λ = h/mv
Electron – Wave like nature
Orbit Orbital
Click here - electron wave
2
nhL
vhmv 2
hmv
2
nhmvr
Combine Bohr and De Broglie
hmv
rn 22
nhmvr
Quantum Model •Electron as standing wave around nucleus •Electron NOT in fixed position •ORBITAL – probability/chance finding electron
mv2 = hf
2
nhr
h
• 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
What does, nλ = 2πr means ?
nλ = 2πr
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
n=1 1λ = 2πr1 ONE wavelength λ fits the 1st orbit
n=2 2λ = 2πr2 TWO wavelength λ fits the 2nd orbit
THREE wavelength λ fits the 3rd orbit 3λ = 2πr3 n=3
nλ = 2πr
1λ
Standing wave around the circumference/circle
TWO wavelength λ fits the 2nd orbit
2λ
THREE wavelength λ fits the 3rd orbit
3λ
ONE wavelength λ fits the 1st orbit
1st Orbit
2nd Orbit
3rd Orbit
n=1 λ1 = 6.3 ao - 1st orbit
2λ2 = 2πr2
3λ3 = 2πr3
n=2
n=3
Relationship between wavelength and circumference
ONE wavelength λ
TWO wavelength λ
THREE wavelength λ
r n = n2 a 0
1λ1 = 2πr1
a o = 0.0529nm/Bohr radius
λ2= 12.6 ao - 2nd orbit
λ3 = 18.9 ao - 3rd orbit
r n = n2 a 0
r n = n2 a 0
1λ
2λ
3λ
Click here to view notes
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
n=1 λ = 2πr1 ONE wavelength λ fits the 1st orbit
n=2 2λ = 2πr2 TWO wavelength λ fits the 2nd orbit
THREE wavelength λ fits the 3rd orbit 3λ = 2πr3 n=3
nλ = 2πr
Click here to view video
λ
Standing wave around the circumference /circle
TWO wavelength λ fits the 2nd orbit
λ
THREE wavelength λ fits the 3rd orbit
λ
ONE wavelength λ fits the 1st orbit
Click here - electron wave simulation
1st Orbit
2nd Orbit
Models for electronic orbitals
1913 1925
Bohr Model
Electron in fixed orbits
De Broglie wavelength
Electron form a standing wave
1927
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
If we know position, x very precisely – we don’t know its momentum, velocity
electron
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
Δx Δx Δx
Δp
Δp = mass x velocity
Velocity is unknown
Position of electron is unknown! Probability/likelyhood to find an electron in space
Big hole Small hole
electron electron
Uncertainty for electron in space
1913 1925
Bohr Model
Electron in fixed orbits
De Broglie wavelength
Electron form a standing wave
1927
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 an electron
ORBITAL is used to replace orbit
If we know position, x very precisely – we don’t know its momentum, velocity
Excellent video on uncertainty principle
Click here video on uncertainty principle Click here to view uncertainty principle
Video on uncertainty principle Δx = uncertainty in position Δp = uncertainty in momentum/velocity (ħ)= reduced plank constant
• Probability finding electron in space • Position electron unknown • Orbital NOT orbit is used
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
• 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
High probability finding electron
✗
Click here to view simulation
Bohr Model Schrödinger's wave function.
better description electron behave
✔
Click here to view simulation
✔ ✗
electron density
Click here to view simulation
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)
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)
Angular Momentum Quantum Number (l): l = 0 to n-1. •Orbital Shape •Divides shells into subshells/sublevels. •Letters (s, d, p, f)
1
2
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
3
4
p orbital s orbital
d orbital
electron spin up/down
writing electron spin
Principal and Angular Momentum Quantum numbers
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)
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
Angular Momentum Quantum Number (l)
Principal Quantum Number (n)
1
2
Principal Quantum #, n (Size , energy)
Angular momentum quantum number, l (Shape of orbital)
n= 1
n= 2
l=0 1s sublevel
l=0
l=1
2s sublevel
2p sublevel
Quantum number, n and l
1 2
1 2
1st energy level Has ONE sublevel
2nd energy level Has TWO sublevels
2s sublevel – contain 2s orbital
2p sublevel – contain 2p orbital
1s sublevel – contain 1s orbital
• 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)
Electronic Orbitals
Principal Quantum #, n (Size , energy)
Angular momentum quantum number, l (Shape of orbital)
Allowed values n = 1, 2, 3,….
n= 1
n= 2
l=0 1s sublevel
Allowed values l = 0 to n-1
l=0
l=1
2s sublevel
2p sublevel
1 2
n= 3 l=1
l=2
l=0 3s sublevel
3p sublevel
3d sublevel
Magnetic Quantum Number (ml) (Orientation orbital)
3
ml =0
ml =0
ml = 0
ml =-1
ml =+1
ml = 0
ml = 0
ml =-1
ml =+1
ml = -l, 0, +l- (2l+ 1 ) for each ℓ value
ml =+1
ml =-1
ml =+2
ml =-2
ml = 0
1s orbital
2s orbital
2px orbital
2py orbital
2pz orbital
3s orbital
3px orbital
3py orbital
3pz orbital
3dxy orbital
3dxz orbital
3dyz orbital
3dz2 orbital
3dx2 – y
2 orbital
Click here to view simulation
Click here to view simulation
Click here to view simulation
Simulation Electronic Orbitals
Energy Level
Quantum Numbers and Electronic Orbitals
n= 1
n= 2
l=0 1s sublevel
l=0
l=1
2s sublevel
2p sublevel
n= 3
l=1
l=2
l=0 3s sublevel
3p sublevel
3d sublevel
ml =0
ml =0
ml = 0
ml =-1
ml =+1
ml = 0
ml = 0
ml =-1
ml =+1
ml =+1
ml =-1
ml =+2
ml =-2
ml = 0
1s orbital
2s orbital
2px orbital
2py orbital
2pz orbital
3s orbital
3px orbital
3py orbital
3pz orbital
3dxy orbital
3dxz orbital
3dyz orbital
3dz2 orbital
3dx2 – y
2orbital
Click here to view simulation
Click here to view simulation
Click here to view simulation
Simulation Electronic Orbitals
Energy Level
Shape
Click here video on quantum number Click here video on quantum number
Concept Map Quantum number
l
4 numbers
No TWO electron have same 4 quantum number
n ms
Electron has special number codes ml
Size/distance Orientation Electron spin
(n,l,ml,,ms) – (1, 0, 0, +1/2) 1s orbital
(n,l,ml,,ms) – (3, 1, 1, +1/2) 3py orbital
Quantum number = genetic code for electron
Electron with quantum number given below
Number + letter
Video on Quantum numbers
1
2 What values of l, ml, allow for n = 3? How many orbitals exists for n=3?
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
What are these 4 numbers? (1, 0, 0, +1/2) or (3, 1, 1, +1/2)