4-2The Quantum Model of the

Atom

Beaker Breaker

1. Who was the scientist that thought electrons can circle the nucleus at set distances…only in allowed paths, or orbits? (solar system model)

2. Now light can also be thought of as a stream of particles called_________

3. ________________spectrum:all wavelengths are present

De Broglie, 1924• If light could behave as both a wave and a particle,

then could an electron (a particle) also behave as both a particle and a wave ?????????????

• He said “YES” because….– Since electrons could only exist at specific energies, and

E can be equated to frequency (E = hν), they have wave properties

– And electrons can be “focused” like light (electron microscopes)

– particle nature of electrons had already been confirmed (cathode rays, oil drop exper, etc.)

Diffraction/Interference

• Diffraction refers to the bending of a wave as it passes by the edge of an object

• Diffraction experiments showed that electron beams, like waves, can interfere with each other.

• Interference occurs when waves overlap.• Overlapping results in a reduction of energy in

some areas and an increase of energy in others.

•Electrons have a dual wave-particle nature

Heisenberg Uncertainty Principle

• It is impossible to determine simultaneously both the position and velocity of an electron or any other particle

Schrodinger Wave Equation, 1926• If electrons have wave properties, then

wave equations can be applied to electrons (and other small particles)

• Laid foundation for quantum theory: describes mathematically the wave properties of electrons and other very small particles

• Gives the probability of finding an electron at a given place in time around the nucleus

Quantum Theory (con’t)• Electrons do NOT travel around the

nucleus like planets around the sun

• Electrons exist in certain regions called orbitals: a 3-D region around the nucleus that indicates the probable location of an electron

Quantum Numbers

• Specify the properties of atomic orbitals and the properties of electrons in orbitals

• There are FOUR quantum numbers….the first three of which come from solutions to Schrodinger’s wave equation

What 2 things does the first quantum # tell us about an atom?

• # energy levels in an atom that the electrons can occupy

• size of the atom

Principal Quantum Number, n

• Indicates the main energy level (or shell) occupied by the electron

• n = 1, 2, 3 etc.

• The ↑n value, the farther the electron is from nucleus prin quant # also gives size info∴

• Total # electrons on a level = 2n2

• Ex: n =2 total electrons = 2(2)2 = 8

• Total # orbitals on a level = n2 since an orbital can hold two electrons (2n2/2= n2)

Angular Momentum Quantum Number, l• Also known as “second quantum number”• Also known as “azimuthal quantum number”• Most energy levels (all but n=1) have orbitals

of different shapes, called sublevels• Describes the shape of the orbital• # orbital shapes possible is equal to the “n”

value– If n=3, then there can be 3 orbital shapes

• The values of l = 0, 1, 2,……. (n-1) – If n=3, then l can be “0”, or “1”, or “2”

1s sublevel

• 1st: probability map (where electrons spend 90% of their time)

• 2nd: surface map ( encloses an area within which the electron spends 90% of its time…10% somewhere outside this surface. Electrons don’t travel on the surface!

s orbital

2p-sublevel

•1st: probability map (where electrons spend 90% of their time)•2nd: surface map ( encloses an area within which the electron spends 90% of its time…10% somewhere outside this surface. Electrons don’t travel on the surface!

Angular Momentum Quantum Number, l (con’t)

• An orbital LETTER is used to designate each shape:

L value Letter designation

0 s (spherical)

1 p (dumbbell)

2 d (complex - p.102)

3 f (too complex for here)

Energy level, n

# sublevels

2nd quant # Letter

denotation

Energy level, n

# sublevels

2nd quant # Letter

denotation

1

Energy level, n

# sublevels

2nd quant # Letter

denotation

1 1 0 s

2

Energy level, n

# sublevels

2nd quant # Letter

denotation

1 1 0 s

2 2 0 s

1 p

3

Energy level, n

# sublevels

2nd quant # Letter

denotation

1 1 0 s

2 2 0 s

1 p

3 3 0 s

1 p

2 d

4

Energy level, n

# sublevels

2nd quant #,l

Letter

denotation

1 1 0 s

2 2 0 s

1 p

3 3 0 s

1 p

2 d

4 4 0 s

1 p

2 d

3 f

What do the first two quantum numbers tell you?

• 1st (principal):

• Size of the orbital

• 2nd (angular momentum):

• Shape of the orbital

Magnetic Quantum Number, ml

• also known as the 3rd quantum number

• indicates the orientation of an orbital around the nucleus

• = (2 l + 1)

s orbital

p orbitals

• 1st of each: probability map (where electrons spend 90% of their time)

• 2nd of each: surface map ( encloses an area within which the electron spends 90% of its time…10% somewhere outside this surface. Electrons don’t travel on the surface!

Three 2p orbitals

“s”

“p”

“d”

d orbitals

f-orbitals 

Magnetic Quantum Number, m (con’t)

• Sum of all orbitals in a sublevel (or E level) is a spherical cloud!

Orbital shape # orientations

s 1

p 3

d 5

f 7

Spin quantum number• Describes the spin of the electron

• Could be either clockwise ( + ½) or counterclockwise (- ½ )

• Each orbital can hold a maximum of two electrons, a pair, spinning in opposite directions

Pauli Exclusion Principle

• No 2 electrons in an atom have the same set of four quantum numbers

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