The Quantum Model The Quantum Model of the Atomof the AtomHonors ChemistryHonors Chemistry

Louie de BroglieLouie de Broglie Proposed that Proposed that all particles of matter that all particles of matter that

move exhibit wave like behaviormove exhibit wave like behavior (even a (even a baseball!)baseball!)

He came up with the following equation He came up with the following equation that relates the wavelength of a particle that relates the wavelength of a particle to its mass and velocity. (Derived from to its mass and velocity. (Derived from E=mcE=mc2 2 and E = hc/and E = hc/))

= = h_ h_ mvmv   Using the Using the mass of an electron mass of an electron moving moving

at the speed of light, he calculated the at the speed of light, he calculated the same energy level values as Bohr did for same energy level values as Bohr did for the Hydrogen atom.the Hydrogen atom.

Louis de BroglieLouis de Broglie De Broglie realized that the De Broglie realized that the

electrons exhibit wavelike electrons exhibit wavelike properties in their quantized properties in their quantized orbits. (draw pictures orbits. (draw pictures ))

He said that if an electron He said that if an electron has wavelike motion and is has wavelike motion and is restricted to circular orbits restricted to circular orbits of a fixed radius, of a fixed radius, the the electron is allowed only electron is allowed only certain possible certain possible wavelengths, wavelengths, frequencies and frequencies and energiesenergies..

Experiments did show that Experiments did show that electrons in atoms do electrons in atoms do exhibit wave behavior with exhibit wave behavior with specific frequencies.specific frequencies.

Standing wave animation

The Heisenberg Uncertainty PrincipleThe Heisenberg Uncertainty Principle Heisenberg concluded that it is impossible Heisenberg concluded that it is impossible

to make any measurement on an object to make any measurement on an object without disturbing it – at least a little.without disturbing it – at least a little.

Electrons are detected by photons and Electrons are detected by photons and because a photon and an electron have the because a photon and an electron have the same energy, any attempt to locate an same energy, any attempt to locate an electron with a photon will knock the electron with a photon will knock the electron off course.electron off course.

Therefore: Therefore: It is impossible to know It is impossible to know both the position and the velocity of an both the position and the velocity of an electron at the same time.electron at the same time.

   So we can only talk about the So we can only talk about the probabilityprobability

of finding and electron in certain area of finding and electron in certain area (remember the fuzzy cloud!)(remember the fuzzy cloud!)

Erwin SchrodingerErwin Schrodinger Used the idea that Used the idea that electrons behave electrons behave

like waveslike waves to write and solve a to write and solve a mathematical equation to describe the mathematical equation to describe the location and energy of an electron in location and energy of an electron in the hydrogen atom.the hydrogen atom.

The modern description of the electron The modern description of the electron cloud in atoms comes from the cloud in atoms comes from the solutions to the Schrodinger equation.solutions to the Schrodinger equation.

This equation showed that the This equation showed that the energyenergy of electrons are restricted to of electrons are restricted to certain values.certain values.

Erwin SchrodingerErwin Schrodinger However, the equation However, the equation does not define does not define

the exact paththe exact path the electron the electron takes takes around the nucleus.around the nucleus.

It only estimates the It only estimates the probabilityprobability of of finding an electron in a certain position, finding an electron in a certain position, unlike Bohr’s circular orbits.unlike Bohr’s circular orbits.

Electrons exist in regions called Electrons exist in regions called OrbitalsOrbitals Orbital Orbital – – 3 dimensional cloud shape 3 dimensional cloud shape

around the nucleus that indicates the around the nucleus that indicates the probable location of an electronprobable location of an electron

Atomic OrbitalsAtomic OrbitalsThe solutions to the The solutions to the

Schrodinger equation are Schrodinger equation are called called Quantum NumbersQuantum Numbers, , and they are used to describe and they are used to describe the properties, such as the the properties, such as the energy level energy level and and shape (s, shape (s, p, d or f)p, d or f), and , and OrientationOrientation of of the atomic the atomic orbitalsorbitals..

““s” - orbitals” - orbital

• Each orbital’s shape is determined by it’s the electron’s energy, which is related to its wavelength!!!!!

““p” orbitalsp” orbitals

An Electron in a p orbital has a different wavelength and therefore a different energy. This gives it a different shape!.

““d” orbitalsd” orbitals

f – orbital = electron has a high energy, short wavelength!

Quantum Number Quantum Number InformationInformation DefinitionDefinition: Set of 4 numbers that : Set of 4 numbers that

tells us the probable location of tells us the probable location of the electron.the electron.

It is like a zip code for the electronIt is like a zip code for the electron The numbers tell us the The numbers tell us the energy energy

levellevel, , shapeshape and and orientationorientation of the of the orbital orbital

And, it tells us the And, it tells us the spin directionspin direction of of the electron in that orbitalthe electron in that orbital

Quantum Number InformationName Definition Symbol Assigned Value

Principle Quantum Number

n

Secondary Quantum Number

l

Magnetic Quantum Number

m

Spin Quantum Number

s

Indicates the main energy level occupied by the electron

Indicates the shape of the orbital occupied by the electron

Indicates the orientation of the orbital around the nucleus

Indicates the spin direction of the electron.

n = 1, 2, 3, . . . 7. .

l = 0 to (n-1)l = 0 “s” orbitall = 1 “p” orbitall = 2 “d” orbital

m = -l to +lIf l = 1Then m = -1, 0 , +1

+½ or -½

Only Only 2 electrons2 electrons are allowed in each are allowed in each orbitalorbital

Each with an opposite spin.Each with an opposite spin. Given the following quantum numbers, Given the following quantum numbers,

describe the “probable” location of the describe the “probable” location of the electron. electron.

n, l, m, s,n, l, m, s, 2, 1, 0, + ½2, 1, 0, + ½ The electron is in energy level 2The electron is in energy level 2 It is in a “p” orbitalIt is in a “p” orbital The orientation of the orbital is the y-The orientation of the orbital is the y-

axisaxis

Quantum # and Atomic StructureQuantum # and Atomic StructureMain Main

Energy Energy Level Level (n)(n)

SublevelsSublevels

(n)(n)

*Orbital *Orbital shapesshapes

# of # of orbitals orbitals per per sublevelsublevel

# # orbitals orbitals per main per main energy energy level (nlevel (n22))

# of # of electrons electrons per per sublevelsublevel

Total # Total # of of electrons electrons per main per main energy energy level level (2n(2n22))

11

22

33

44

s 1 1 2 2

s

p

1

3 4s= 2

p= 68

s

p

d

135

9 18

s= 2

p = 6

d = 10

s

p

d

f

1

3

5

7

16s = 2

p = 6

d = 10

f = 14

32