Quantum Mechanics Chapter 4 CPS Chemistry. Objectives Discuss the wave-particle nature of light Describe the photoelectric effect Discuss how electrons.

Quantum Mechanics

Chapter 4

CPS Chemistry

Objectives

Discuss the wave-particle nature of lightDescribe the photoelectric effectDiscuss how electrons act as wavesDiscuss the development of the quantum

model of the atomWhat is Heisenberg Uncertainly principleWho was Schrodinger?

Light as a Particle

Visible light is a kind of electromagnetic radiation that exhibits wave like behavior as it moves through space.

All electromagnetic radiation moves at the same speed in a vacuum 3.0x108m/s(speed of light)

Photoelectric Effect

Albert Einstein found that if you shined light on a piece of metal with the correct frequency that electrons would be knocked off, creating an electric current. Which could be detected like voltage flowing from a battery

This is called the Photoelectric Effect, which Albert Einstein won the Nobel Prize for in 1921*

*Note Nobel Prizes can be awarded years or decades after important discoveries have been made

Quantum

Max Plank found in the early 1900’s that the release of light by hot objects (think filament in a light bulb) does not release energy in a stream (think water from a hose), but in small packets of energy (think the energy to throw a tennis ball) called Quanta (plural)

A quantum is the minimum quantity of energy that can be lost or gained by an atom(energy needed to throw 1 tennis ball)

Quantum II

The vehicle for this energy is called a Photon, a mass-less particle of electromagnetic radiation (Think, tennis ball)

Ground & Excited states

Electrons exist at certain levels outside the nucleus of the atom, the further away from the nucleus the higher the energy

When a electron goes from an excited state (higher level) to a lower level, it releases energy in form of a photon, or light, each element has its own “signature” or frequency of light. It is this color(s) of light that allow us to identify different elements

To get an electron to leave a ground state to go to a higher state you must add energy

Electrons as Waves

So far we have discussed how light can act as a particle, but conversely particles can act as waves

Work by deBroglie found that electrons around the nucleus of an atom exhibited wave behavior, acting at certain frequencies around the nucleus

Further experiments proved more wavelike behavior such as a stream of electrons can be bent (diffracted), or that two electron beams can interfere with each other, just like water waves.

Heisenburg’s Experiment

The idea that electrons sometimes acted like particles and other times acted like waves was very confusing for scientists.

Werner Heisenburg had an experiment where he tried to detect the exact location of an electron by hitting them with photons (about the same energy as an electron) like pool balls on a pool table. But with this method it was hard to pinpoint the location of any particular electron,

Heisenburg Uncertainty Principle

Through his experiment Heisenburg found that it was impossible to know both the location AND the speed of any particular electron simultaneously

Schrödinger Wave Equation

Schrödinger found that only specific energies for electrons made them act like waves, not ALL energies.

Schrodinger & Heisenburg’s work laid the foundation for modern quantum theory

Atomic Orbitals & Quantum Numbers

First, you must think of an atom 3-dimensionally, that electrons live in not only an x-y space but also in a z direction

Quantum numbers are the “address” of an electron in relation to the nucleus

Each electron has an “address” of a unique combination of 4 quantum numbers

Principle Quantum number - N

N is the principle quantum number, it represents the energy level of the electron, or how far away it is from the nucleus

N can be a positive integer, 1, 2, 3, etc. The bigger the number, the higher the energy

and the further it is from the nucleus More than one electron can have the same N

quantum number, if they are in the same “Shell” or level. The total number of orbitals in a shell is equal to N2

Angular Momentum QN

Angular Momentum describes the shape of the of the sublevels of the orbital

L value tells you the shape of the orbital, the number of shapes possible is equal the principle QN Example

When n = 1, there is one shape (sphere) When n = 2 there are two shapes (sphere & dumbbell) When n = 3 there are three shapes (sphere, dumbbell,

and flower)

Values of L

L can be zero or any positive integer, example 0,1,2,3, up to n-1

So if n = 2 than the possible values for L are 0 and 1, since the highest value is n-1

What if n=4 what are the values of L? 0,1,2,3 since 3 = N-1= 4-1(=3) Understand that quantum numbers explain where the

likelihood of an electron to be, but due to Heisnburg’s uncertainty principle we can not know exactly where a particular electron is at any given time.

Shapes of L

Each value of L corresponds to a different shape of the orbital, and each shape has its own identifying letter

0 is the s orbital and has a sphere shape 1 is the p orbital and has a dumbbell shape

(three orientations: x,y,z) 2 is the d orbital and has a flower shape and has

many different orientations 3 is the f orbital and has a bizarre shapes that

can not easily be described.

Orientation of L

The magnetic quantum number explains the orientation or the orbital around the nucleus

For the s orbital there is only on orientation M = 0

For the p orbital there are 3 orientations M = -1,0,1

For the d orbital there are 5 orientations M= -2,-1,0,1,2

For the f orbital there are 7 orientations M= -3,-2,-1,0,1,2,3

Spin Quantum Number

Lastly, electrons in their orbitals also spin, and the spin of the electron can be described in two ways +1/2 and –1/2

An orbital can have at most 2 electrons, therefore they must have opposite spins

Review of Quantum numbers

N: Principle, describing how far from nucleus. N=1,2,3,4,etc.

L: Angular Momentum, describing the shape of the orbital. L = 0,1,2,3…n-1 S,p,d,f

M: Magnetic, describing the orientation around the nucleus

Sp: Spin, either +½ or - ½ Each electron needs a UNIQUE set of Quantum

Numbers