SPARKS

CH301

Why are there no blue fireworks?

LIGHT, ELECTRONS & QUANTUM MODEL

UNIT 2 Day 2

LM15, 16 & 17 due W 8:45AM

Which of these types of light has the highest energy photons ?

A. “Green” Light (540 nm or 5.4 x 10-7 m) B. “Red” Light (650 nm or 6.5 x 10-7 m) C. Radio waves (100 m) D. Ultraviolet (50 nm or 5 x 10-8 m) E. Infrared (3 mm or 3 x 10-6 m)

QUIZ: CLICKER QUESTION

Quick Review of DNA

Why Should I wear Sunscreen?

TYPES of DNA DAMAGE

Why Should you wear Sunscreen?

AVOBENZONE – common active ingredient, UVmax 357 nm

Zinc Oxide – reflects UV light

• We shine a beam of light with energy 7 eV on a gold surface (Φ = 5.1 eV) and measure the number and KE of electrons that are ejected. If we increase the energy of our incident radiation (the beam of light), what would you expect to happen?

A. More electrons would be ejected.

B. Fewer electrons would be ejected.

C. The ejected electrons would have a higher KE.

D. The ejected electrons would have a lower KE.

E. Both answers (A) and (C) would be expected.

QUIZ: CLICKER QUESTION

What are we going to learn today?

• Understand how light can probe electrons in atoms

• Recognize that electrons have discrete energy levels in

atoms

• Predict the energy for transitions of an electron between

the energy levels in hydrogen

• Relate the empirical model to the theoretical model of the

energy levels of electrons in H atom

• Solutions to the theoretical model predict electron

configuration

The Simplest Atom - Hydrogen

What do we know about the H electron?

Exciting Electrons Demo

Exciting Electrons Demo

Exciting Electrons Demo

Exciting Electrons Demo

Think Like a Chemist

HH HH

H* H*

H* H*

Ne*

Ne*

Ne Ne

Exciting Electrons Demo

POLLING: CLICKER QUESTION

WHICH SPECTRUM WOULD YOU EXPECT TO SEE IF WE WERE TO PUT A GRATING BETWEEN YOU AND THE LIGHT SOURCE?

A.

B.

Based on the colors you see in the demo, exciting which gas leads to emission of the the highest energy visible photons? a) He b) H2 c) Ne

POLL: CLICKER QUESTION

Rydberg Formula

Mathematician Balmer noted a pattern in the frequencies of some of the lines. Rydberg figured this out with an Empirical model for all the lines for the H-atom (simple because there is only one electron)

Convert wavelength to frequency to energy n1 and n2 are Integers!

E is proportional to 1/n2

Where do these Energy levels come from?

Rydberg Formula

Discrete lines = Discrete Energies Particular wavelengths correspond to transitions between different energy levels. NOT ALL ENERGIES ARE POSSIBLE! What is the energy difference between the n=1 and n=2 states

Negative corresponds to emission Positive to absorption

n1 and n2 are Integers!

For n=2 to n=1 Energy given off or absorbed by atom? Higher E to lower E Delta E = -2.18 x 10^-18 * (1-0.25) Delta E = negative.

THIS INTERPRETATION OF THE LINE SPECTRA SUGGESTED

THAT THE ENERGIES OF THE ELECTRONS MUST BE QUANTIZED!

Electrons in hydrogen atoms must have only

specific allowed energies because only specific changes in energy (ΔE) are observed.

Bohr’s model- solar system -EMPIRICAL

• Bohr’s theory allowed for the calculation of an energy level

• Or the calculation of the emitted wavelength upon release of energy when an electron transitions from higher to lower energy

ΔE = h(c/λ)

ATOMIC EMISSION LINE SPECTRA

hydrogen

calcium

helium

sodium

http://astro.u-strasbg.fr/~koppen/discharge/

• In order for an electron to move to a different energy level in an atom, what must happen?

a. Nothing. Electrons don’t move to different energy levels

b. The electron must absorb energy

c. The electron must give off a photon

d. The electron must either absorb or give off energy

POLLING: CLICKER QUESTION

You have two samples of the same gas. Sample X has ten times more atoms than sample Y. How will their emission spectra compare?

a. Sample X’s spectrum will have more colors.

b. Sample X’s spectrum will have brighter colors.

c. Sample X’s spectrum will have both more colors and brighter colors.

d. We would expect no difference between the two spectra.

POLLING: CLICKER QUESTION

• Bohr model was not working well for an atom with more than one electron. It treated the electron as a particle.

• de Broglie had shown that electrons have wave properties.

• Schrödinger decided to emphasize the wave nature of electrons in an effort to define a theory to explain the architecture of an atom.

BOHR MODEL

http://upload.wikimedia.org/wikipedia/commons/c/cf/Circular_Standing_Wave.gif

Heisenberg Uncertainty Principle

• Wavelike properties of very small matter means that we cannot simultaneously determine the location of the particle and exactly how it is moving (momentum).

• Δp Δx > constant

• Δp Δx > ½ ħ

Wave-Particle Duality

Small (low mass) “particles” have wave-like properties They are neither described as particles or waves They have characteristics of each. We saw the same issue for “light” Seems like a wave, but the energy (photon) appears particle-like

How do we deal with the new “wave/particle”

things? We need a new model!!

Quantum Mechanics! It doesn’t make sense! It shouldn’t! You don’t live in a world of tiny particles with vanishingly small mass and momentum. It is what it is.

Wave functions – Tell us about “where” the electron is. (the probability of finding the particle at a given position)

Energies– Tell us about the energy of the electron

The Schrödinger Equation allows us to solve for all possible wavefunctions and energies

The Hydrogen Atom

Simplest of all atomic problems. 1 proton, 1 electron.

Put that into the Schrödinger Equation and solve

Wavefunctions and energies

Function Machine (Schrödinger Equation)

That will give us the solutions

The Hydrogen Atom

Infinite number of solutions Which solution are we are interested in? LOWEST ENERGY GROUND STATE ELECTRON CONFIGURATION

Function Machine (Schrödinger Equation)

That will give us the solutions

Where is the Energy?

Two key ideas from Quantum Mechanics, systems are described by

Energies– Tell us about the energy of the electron

DIAGRAM SOLUTIONS LOWEST ENERGY ELECTRON TO HIGHEST ENERGY ELECTRON (Draw energy level diagram for hydrogen atom)

ENERGY

• Rydberg-from Bohr model:

= R(1/n12 – 1/n2

2)

(R = 3.29 X 1015 Hz)

• Schrödinger calculated actual energy of the e- in H using his wave equation with the proper expression for potential energy

En = -hR/n2 = -2.18 x 10-18 J/n2

• n is principal quantum number which is an integer that labels the different energy levels

• e- will climb up the energy levels until freedom – ionization n = ∞

IONIZATION VERSUS PHOTOELECTRIC EFFECT

Where is the particle?

Two key ideas from Quantum Mechanics, systems are described by

Wave functions – Tell us about “where” the electron is. (the probability of finding the particle at a given position)

WAVE FUNCTION

• Schrödinger replaced precise trajectory of a particle with a wave function.

• Born interpretation of the wave function- the probability of finding the particle in a region is proportional to the value of ψ2

• Ψ2 = probability density – probability that a particle will be found in a region divided by the volume of the region

• Ψ2 = 0 indicates node

Physical Model – Quantum Mechanics

Electrons are they particles? Are they waves? Neither! They are strange quantum mechanical things that appear to us sometimes as being particles and sometimes as waves

CH301 Vanden Bout/LaBrake Fall 2013

SOLUTIONS: Atomic Orbitals

• Apply wave function to e- in 3-D space, bound by nucleus.

• Solutions to these wave equations are called orbitals.

• Wave function squared gives the probability of finding the electron in that region in space.

• Each wave function is labeled by three quantum numbers,

– n – size and energy

– l – shape

– ml – orientation

Atomic orbitals: defined by Quantum Numbers

• PRINCIPAL quantum number, n.

– Describes the energy and approximate nuclear distance.

– Shell

– n = 1, 2, 3, 4, ......

• ANGULAR MOMENTUM quantum number, l.

– Describes the shape of the orbital

– orbitals of a shell fall into n groups called subshells

– l = 0, 1, 2,.......(n-1)

– l = s, p, d, f,......

Shapes are hard to draw

At the moment we really care about the wavefunction squared often called the probability density. Radial probability density is the probability of finding the electron at some distance from the nucleus

Hydrogen Like atoms

Below is a plot of the radial distribution of He+, and H (both have only 1 electron) Which is He+?

POLLING: CLICKER QUESTION

Classify the solutions

Classify our wavefunction solutions based upon both Energy - principle quantum number n “Shape” - angular momentum quantum number l

Shapes are hard to draw

How do we draw three dimensional functions? It is hard. http://winter.group.shef.ac.uk/orbitron/

s orbital – actually 1s is “easy” to draw

s-orbitals

Solutions Shapes (where is the electron?)

These are the n = 2 solutions, which one of

these is not like the others?

• MAGNETIC quantum number, ml.

– indicates the orientation of the angular momentum around the nucleus

– distinguishes different orbitals within a subshell

– The number of values of ml gives you the number of orbitals for a given subshell.

– ml = integers from –l through 0 to + l.

– there are 2l + 1 values of ml for a given value of l

p-orbitals

Probability distribution of p orbital

3 different orientations of p subshell, denoted by the three values of ml

A cross section of the electron probability distribution for a 3p orbital.

d-orbitals

Probability distribution distribution of d orbital

5 different orientations of d orbitals

denoted by 5 different values of ml

f-orbitals

7 different orientations of f orbitals denoted by the seven different values for ml

What Did We Learn Today?

LIGHT CAN BE USED TO PROBE THE ENERGY OF ELECTRONS IN MATTER Developed a physical model that predicts the energy of electron in H atom - QUANTUM

Learning Outcomes

Understand QM is a model and that solutions to the Schrödinger equation yield wave functions and energies Understand that the wave function can be used to find a radial distribution function that describes the probability of an electron as a function of distance away from the nucleus List, define and describe the three quantum numbers for the H-atom wave functions and know what possible combinations of quantum numbers are allowed. Define the atomic orbital names based on quantum numbers