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**Chapter 13 Electrons in Atoms**

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**Section 13.1 Models of the Atom**

OBJECTIVES: Summarize the development of atomic theory.

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**Section 13.1 Models of the Atom**

OBJECTIVES: Explain the significance of quantized energies of electrons as they relate to the quantum mechanical model of the atom.

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**J. J. Thomson’s Model Discovered electrons**

Negative electron floating around “Plum-Pudding” model

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**Ernest Rutherford’s Model**

Discovered dense positive piece at the center of the atom- nucleus “Nuclear model”

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**Niels Bohr’s Model Move like planets around the sun.**

In circular orbits at different levels. Amounts of energy separate one level from another. “Planetary model”

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**Bohr’s planetary model**

electron cannot exist between energy levels, just like you can’t stand between rungs on ladder Quantum of energy required to move to the next highest level

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**The Quantum Mechanical Model**

Since the energy of an atom is never “in between” there must be a quantum leap in energy. Erwin Schrodinger Mathematical solution

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**The Quantum Mechanical Model**

Has energy levels for electrons. Orbits are not circular. It can only tell us the probability of finding an electron a certain distance from the nucleus.

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**The Quantum Mechanical Model**

The atom is found inside a blurry “electron cloud” An area where there is a chance of finding an electron. Think of fan blades

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Atomic Orbitals Principal Quantum Number (n) = the energy level of the electron. Within each energy level, the complex math of Schrodinger’s equation describes several shapes. Atomic orbitals - regions where there is a high probability of finding an electron. Sublevels

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**Summary # of shapes Max electrons Starts at energy level s 1 2 1 p 3 6**

d 5 10 3 7 14 4 f

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**By Energy Level First Energy Level only s orbital only 2 electrons 1s2**

Second Energy Level s and p orbitals are available 2 in s, 6 in p 2s22p6 8 total electrons

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**By Energy Level Third energy level s, p, and d orbitals**

2 in s, 6 in p, and 10 in d 3s23p63d10 18 total electrons Fourth energy level s,p,d, and f orbitals 2 in s, 6 in p, 10 in d, ahd 14 in f 4s24p64d104f14 32 total electrons

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**Section 13.2 Electron Arrangement in Atoms**

OBJECTIVES: Apply the aufbau principle, the Pauli exclusion principle, and Hund’s rule in writing the electron configurations of elements.

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**Section 13.2 Electron Arrangement in Atoms**

OBJECTIVES: Explain why the electron configurations for some elements differ from those assigned using the aufbau principle.

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**Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p**

Aufbau diagram - page 367

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**Electron Configurations**

Aufbau principle- electrons enter the lowest energy first. This causes difficulties because of the overlap of orbitals of different energies. Pauli Exclusion Principle- at most 2 electrons per orbital - different spins

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**Electron Configuration**

Hund’s Rule- When electrons occupy orbitals of equal energy they don’t pair up until they have to. Phosphorus (15 electrons)

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**Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p**

The first two electrons go into the 1s orbital Notice the opposite spins only 13 more to go...

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**Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s**

The next electrons go into the 2s orbital only 11 more...

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**Increasing energy The next electrons go into the 2p orbital**

3d 4d 5d 7p 6d 4f 5f The next electrons go into the 2p orbital only 5 more...

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**Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s**

The next electrons go into the 3s orbital only 3 more...

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**Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s**

The last three electrons go into the 3p orbitals. They each go into separate shapes 3 unpaired electrons = 1s22s22p63s23p3

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**The easy way to remember**

2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2 electrons

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**Fill from the bottom up following the arrows**

2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 4 electrons

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**Fill from the bottom up following the arrows**

2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 2p6 3s2 12 electrons

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**Fill from the bottom up following the arrows**

2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 2p6 3s2 3p6 4s2 20 electrons

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**Fill from the bottom up following the arrows**

2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 38 electrons

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**Fill from the bottom up following the arrows**

2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 56 electrons

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**Fill from the bottom up following the arrows**

2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 88 electrons

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**Fill from the bottom up following the arrows**

2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6 108 electrons

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**Exceptional Electron Configurations**

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**Orbitals fill in order Lowest energy to higher energy.**

Adding electrons can change the energy of the orbital. Half filled orbitals have a lower energy. Makes them more stable. Changes the filling order

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**Write these electron configurations**

Titanium - 22 electrons 1s22s22p63s23p64s23d2 Vanadium - 23 electrons 1s22s22p63s23p64s23d3 Chromium - 24 electrons 1s22s22p63s23p64s23d4 expected But this is wrong!!

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**Chromium is actually: 1s22s22p63s23p64s13d5 Why?**

This gives us two half filled orbitals. Slightly lower in energy. The same principal applies to copper.

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**Copper’s electron configuration**

Copper has 29 electrons so we expect: 1s22s22p63s23p64s23d9 But the actual configuration is: 1s22s22p63s23p64s13d10 This gives one filled orbital and one half filled orbital. Remember these exceptions: d4, d9

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**Section 13.3 Physics and the Quantum Mechanical Model**

OBJECTIVES: Calculate the wavelength, frequency, or energy of light, given two of these values.

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**Section 13.3 Physics and the Quantum Mechanical Model**

OBJECTIVES: Explain the origin of the atomic emission spectrum of an element.

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Light The study of light led to the development of the quantum mechanical model. Light is a kind of electromagnetic radiation. Electromagnetic radiation includes many kinds of waves All move at 3.00 x 108 m/s = c

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Parts of a wave Crest Wavelength Amplitude Origin Trough

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**Parts of Wave - p.372 Origin - the base line of the energy.**

Crest - high point on a wave Trough - Low point on a wave Amplitude - distance from origin to crest Wavelength - distance from crest to crest Wavelength is abbreviated by the Greek letter lambda = l

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Frequency The number of waves that pass a given point per second. Units: cycles/sec or hertz (hz or sec-1) Abbreviated by Greek letter nu = n c = ln

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**Frequency and wavelength**

Are inversely related As one goes up the other goes down. Different frequencies of light are different colors of light. There is a wide variety of frequencies The whole range is called a spectrum, Fig , page 373

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Low energy High energy Radiowaves Microwaves Infrared . Ultra-violet X-Rays GammaRays Low Frequency High Frequency Long Wavelength Short Wavelength Visible Light

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**Atomic Spectrum Each element gives off its own characteristic colors.**

Can be used to identify the atom. How we know what stars are made of.

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**These are called discontinuous spectra, or line spectra**

unique to each element. These are emission spectra The light is emitted given off Sample 13-2 p.375

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**Light is a Particle Energy is quantized. Light is energy**

Light must be quantized These smallest pieces of light are called photons. Photoelectric effect? Energy & frequency: directly related.

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**Energy and frequency E = h x E is the energy of the photon**

is the frequency h is Planck’s constant h = x Joules x sec. joule is the metric unit of Energy

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The Math in Chapter 13 2 equations so far: c = E = h Know these!

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Examples What is the wavelength of blue light with a frequency of 8.3 x 1015 hz? What is the frequency of red light with a wavelength of 4.2 x 10-5 m? What is the energy of a photon of each of the above?

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**Explanation of atomic spectra**

When we write electron configurations, we are writing the lowest energy. The energy level, and where the electron starts from, is called it’s ground state- the lowest energy level.

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Changing the energy Let’s look at a hydrogen atom

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Changing the energy Heat or electricity or light can move the electron up energy levels (“excited”)

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Changing the energy As the electron falls back to ground state, it gives the energy back as light

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**Changing the energy May fall down in steps**

Each with a different energy

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Ultraviolet Visible Infrared Further they fall, more energy, higher frequency. This is simplified the orbitals also have different energies inside energy levels All the electrons can move around.

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**What is light? Light is a particle - it comes in chunks.**

Light is a wave- we can measure its wavelength and it behaves as a wave If we combine E=mc2 , c=, E = 1/2 mv2 and E = h We can get: = h/mv called de Broglie’s equation Calculates the wavelength of a particle.

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Sample problem What is the approximate mass of a particle having a wavelength of 10-7 meters, and a speed of 1 m/s? Use = h/mv = 6.6 x 10-27 (Note: 1 J = N x m; 1 N = 1 kg x m/s2

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**Matter is a Wave Does not apply to large objects**

Things bigger than an atom A baseball has a wavelength of about m when moving 30 m/s An electron at the same speed has a wavelength of 10-3 cm Big enough to measure.

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