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

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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

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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

✗

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Bohr Model Schrödinger's wave function.

better description electron behave

✔

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✔ ✗

electron density

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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

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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

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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)