Chapter 8: Electrons in Atoms Or Quantum Mechanics Made Simple?

1 Chapter 8: Electrons in Atoms Or Quantum Mechanics Made Simple? I. Introduction to Electronic Structure A. Interaction of Light and Matter 1. Prop...
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Chapter 8: Electrons in Atoms Or Quantum Mechanics Made Simple? I.

Introduction to Electronic Structure A. Interaction of Light and Matter 1. Properties of Light 2. Absorption and Emission of Light 3. The Bohr Model of the Atom II. Quantum Mechanics A. The H-atom 1. Atomic Orbitals and Quantum #’s 2. Shapes of Orbitals B. Many Electron Atoms-Another Quantum # C. Electron Configurations and the Periodic Table

https://upload.wikimedia.org/wikipedia/commons/a/a0/Military_laser_experiment.jpg, http://2012books.lardbucket.org/books/principles-of-general-chemistryv1.0/section_10/16fa8010753f93c33b628613f15d3a25.jpg

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I. Introduction to Electronic Structure

A. Interaction of Light and Matter 1. Properties of Light (Electromagnetic Radiation)

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Terms Used to Describe Waves How do we know light travels in waves?

- it can be reflected, refracted, and diffracted

1. wavelength() –

distance between successive peaks (measured in nm for the light we do chemistry with)

2. frequency() –

number of wavelengths that pass a given point per unit time, measured in cycles per second, s-1 (Hz)

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3. Amplitude –

maximum height of a wave (related to the intensity or brightness of the light, really the square of the amplitude)

Range of Wavelengths/Frequencies

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Relationship Between λ , ν, and c Units – wavelength usually given in nm, but must be converted to m for calculations Example #1 The light from red LEDs is commonly seen in many electronic devices. A typical LED produces 6.90x102 nm light. What is the frequency of this light?   6.90x10 2 nm c  2.998x10 8

m s

c    1m  6.90 x10 7 m 9 1x10 nm m 2.998 x108 c s  4.34 | 49 x1014 1  4.34 x1014 Hz    6.90 x10 7 m s

  6.90x10 2 nm 

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Chemistry With Light UV Light

Visible Light

IR Light

Microwaves

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Energy of Light How much energy does light possess?

Energy of Quantum of Light E =constant x frequency Constant = h = Planck’s constant = 6.626 x 10-34 J-s Calculate Energy of a quantum of Light E = hν h = plancks constant

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What is a Quantum of Light (Particle Nature of Light) Photoelectric effect –

the ejection of electrons from a metal surface when it is irradiated with UV radiation

Observations of the Photoelectric Effect 1. no electrons ejected unless the radiation has a certain minimum energy (frequency) (each metal is different) 2. electrons are emitted immediately, regardless of the intensity of the radiation 3. K.E. of ejected electrons increases linearly with increasing frequency of radiation Einstein’s Conclusions 1. Radiation striking metal surface behaves like a particle 2. Energy of photon = h  radiation is quantized (same as that described by Planck) http://www.deism.com/images/Einstein_laughing.jpeg, https://sakai.ithaca.edu/access/content/user/jkleingardner/Principles%20HTML%20slides/img/ch2/PhotoelectricEffect.jpg

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Example Problem #2 Calculate the energy of one photon of UV light that has a wavelength of 280 nm. What is the energy contained in a mole of these photons? Is this enough energy to break a C-Cl bond in CCl3F (B.E. = 5.06x10-19 J)? (CFC-11 45 years)

  280 nm  280 nm 

1m 7  2 . 80 x 10 m 9 1x10 nm

6.626 x1034 J  s  2.998x108 m / s 19 E  hv    7 . 09 | 45 x 10 J 7  2.80 x10 m hc

= 7.09x10-19 J Yes, it does have enough energy to break the C-Cl bond.

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2. Absorption and Emission of Light (How do Matter and Light Interact?) What happens when atoms gain energy?

What happens when atoms lose energy?

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Terms Wavelength Spectrum – Continuous Spectrum – Line Spectra –

radiation separated into its components spectrum containing all wavelengths

only certain wavelengths produced and separated

Information from light emission

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What is really going on?

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3. Bohr Model of the Atom 1.

Electrons move in circular orbits around the nucleus.

2.

There are only certain allowed orbitals.

3.

In order for an electron to move between orbitals it must gain/lose the right magnitude of energy.

Absorption and Emission of Light from Atoms (Qualitative)

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Good and Bad of the Bohr Model Good – Electrons do reside in quantized orbitals, described by quantum numbers Energy is given off or absorbed when electrons move between energy levels Bad – Doesn’t work for multiple electron atoms Doesn’t incorporate wave-like properties of electrons

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II. Quantum Mechanics Matter and Waves De Broglie – if radiation is particle-like and wave-like then perhaps all matter has both types of properties 

h mv

Comparison Electron m = 9.11x10-31 kg v = 1x107 m/s  = 7x10-11 m (7x10-2 nm)

Baseball m = 0.10 kg v = 45 m/s (100 mph)  = 1.5x10-34 m (1.5x10-25 nm)

Uncertainty Principle - If matter travels in waves how do we know where it is? Uncertainty principle – It is impossible to know the exact position and momentum (mv) of a particle

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Uncertainty Principle Cont’d Mathematically -

h x  mv  4

x = uncertainty in position mv = mv = mass times uncertainty in velocity Example Problem The electron has a mass of 9.11x10-31 kg. Assume we know the speed of the electron to be 5x106 m/s and this value has an uncertainty of 1%. What is the uncertainty in position of the electron? h h x  mv  x  4 4  mv m  9.11x10-31 kg v  .01 5x10 6 m / s  5 x104 m / s m2 34 6.63x10 kg  2  s 9 s x   1 x 10 m -31 4 4  9.11x10 kg  5 x10 m / s 2. Quantum Mechanics Radius of H-atom = 1x10-10 m

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A. The H-atom 1. Atomic Orbitals and Quantum #’s Schrödinger Wave Equation 1-dimensional – 1 variable (1 quantum #)  2 d 2   V ( x)  E 2m dx 2

3-dimensional – 3 variables (3 quantum #’s)  2  d 2 d 2 d 2    2  2  2   V ( x, y, z )  E 2m  dx dy dz 

m = mass of particle ђ = planck’s constant / 2 Orbital –

Me

describes the regions in an atom where the probability of finding an electron is high (found by squaring the wave function) H-atom

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Orbitals Atom -

an apartment building for electrons

S’s Equation - provides 3 identifying properties that help us locate an electron

Apt analogy Atom

n

n

l

ml

floor

# of apt on each floor shape of space e- can occupy

# of rooms in each apt # of orbitals of a specific shape

distance from nucleus

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l

Mention Name and Shape Value of l 0 1 Letter s p

2 d

3 f

4 g

5 h

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ml

Representation of Some Orbitals For H n=1 n =2 n=3 l=0 l=0 l=1 l=0 l=1 1s

2s

ml = 0

0

2p

-1

3s

0

1

0

3p

-1

0

l=2 3d

1

-2 -1 0 1 2