# Chapter 13 Electrons in Atoms

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Chapter 13 Electrons in Atoms

Section 13.1 Models of the Atom
OBJECTIVES: Summarize the development of atomic theory.

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.

J. J. Thomson’s Model Discovered electrons
Negative electron floating around “Plum-Pudding” model

Ernest Rutherford’s Model
Discovered dense positive piece at the center of the atom- nucleus “Nuclear model”

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”

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

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

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.

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

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

Summary # of shapes Max electrons Starts at energy level s 1 2 1 p 3 6
d 5 10 3 7 14 4 f

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

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

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.

Section 13.2 Electron Arrangement in Atoms
OBJECTIVES: Explain why the electron configurations for some elements differ from those assigned using the aufbau principle.

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p
Aufbau diagram - page 367

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

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

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...

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...

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...

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...

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

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

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

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

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

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

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

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

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

Exceptional Electron Configurations

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

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

Chromium is actually: 1s22s22p63s23p64s13d5 Why?
This gives us two half filled orbitals. Slightly lower in energy. The same principal applies to copper.

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

Section 13.3 Physics and the Quantum Mechanical Model
OBJECTIVES: Calculate the wavelength, frequency, or energy of light, given two of these values.

Section 13.3 Physics and the Quantum Mechanical Model
OBJECTIVES: Explain the origin of the atomic emission spectrum of an element.

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

Parts of a wave Crest Wavelength Amplitude Origin Trough

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

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

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

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

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.

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

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.

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

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

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?

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.

Changing the energy Let’s look at a hydrogen atom

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

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

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.

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.

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

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.