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Electrons in Atoms

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**Dalton’s Atomic Theory**

John Dalton ( ) had four theories All elements are composed of submicroscopic indivisible particles called atoms Atoms of the same element are identical. The atoms of anyone element are different from those of any other element Atoms of different elements can physically mix together or can chemically combine w/ one another in simple whole-number ratios to form compounds Chemical reactions occur when atoms are separated, joined, or rearranged. However, atoms of one element are never changed into atoms of another elements as a result of a chemical reaction

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**Thomson’s Atomic Model**

Thomson though electrons were like plums embedded in a positively charged “pudding”, so his model was called the “plum pudding” model

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Thomson’s Theory Thomson stated: The atom had negatively charged electrons stuck into a lump of positively charged protons. Thomson never explained Number of protons and neutrons The arrangement of the particles in the atom The ease with which atoms are stripped of electrons to form ions

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**Rutherford Model Rutherford used the Gold Foil Experiment**

Rutherford proposed the following: Thomson model was incorrect Most of the mass of the atom and all of its positive charge reside in a very small, extremely dense region, which he called the nucleus Most of the total volume of the atom is empty space in which electrons move around the nucleus

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Rutherford’s Model Discovered dense positive piece at the center of the atom Nucleus Electrons moved around Mostly empty space

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Bohr Model Bohr changed the Rutherford model and explained how the electrons travel. Bohr explained the following in his model: Electrons travel in definite orbits around the nucleus Electrons are arranged in concentric circular paths or orbitals around the nucleus Electrons don’t fall into the nucleus because electrons in particular path have fixed energy and don’t lose energy His model was patterned after the motion of the planets around the sun. It is often called the Planetary model.

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Bohr Model Cont.

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Bohr’s Model Nucleus Electron Orbit Energy Levels

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Quantum Theory Bohr explained how electrons were moving via Quantum Theory Key Terms: Energy Levels- Regions around the nucleus where the electron is likely moving Quantum- Amount of energy required to move an electron from one energy level to the next Quantum Leap- Abrupt Change

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**} Bohr’s Model Fifth Fourth Increasing energy Third Second First**

Further away from the nucleus means more energy. There is no “in between” energy Energy Levels Fifth Fourth Third Increasing energy Second First Nucleus

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**Bohr’s Model cont. Energy levels are not equally spaced.**

Energy levels more closely spaced further from the nucleus Higher energy level occupied by an electron, the more energetic that electron is. Amount of energy gained or lost by an electron is not always the same amount.

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**Bohr Model Cont. The Bohr Model did not account for:**

Emission spectra of atoms containing more than one electron. So comes along the next model:

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**The Quantum Mechanical Model**

Energy is quantized. It comes in chunks. A quanta is the amount of energy needed to move from one energy level to another. Since the energy of an atom is never “in between” there must be a quantum leap in energy. Schrodinger derived an equation that described the energy and position of the electrons in an atom

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**The Quantum Mechanical Model**

Things that are very small behave differently from things big enough to see. The quantum mechanical model is a mathematical solution It is not like anything you can see.

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Wave Functions Erwin Schrödinger: We can describe the electron mathematically, using quantum mechanics (wave mechanics). Schrödinger developed a wave equation to describe the hydrogen atom. An acceptable solution to Schrödinger’s wave equation is called a wave function. A wave function represents an energy state of the atom.

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**Schrödinger’s Equation**

The wave function is a F(x, y, z) Actually F(r,θ,φ) Solutions to the equation are called orbitals. These are not Bohr orbits. Each solution is tied to a certain energy These are the energy levels Animation

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**Schrödinger’s Equation**

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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” A area where there is a chance of finding an electron. Draw a line at 90 %

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**The Uncertainty Principle**

Werner Heisenberg: We can’t know exactly where a moving particle is AND exactly how fast it is moving at the same time. The photon that will enter the microscope, so that we might “see” the electron … … has enough momentum to deflect the electron. The act of measurement has interfered with the electron’s motion.

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**The Uncertainty Principle**

A wave function doesn’t tell us where the electron is. The uncertainty principle tells us that we can’t know where the electron is. However, the square of a wave function gives the probability of finding an electron at a given location in an atom. Analogy: We can’t tell where a single leaf from a tree will fall. But (by viewing all the leaves under the tree) we can describe where a leaf is most likely to fall.

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Atomic Orbitals There are the region of space which there is a high probability of finding an electron Within each energy level the complex math of Schrodinger’s equation describes several shapes. These are called atomic orbitals Quantum Numbers- numbers that specify the properties of atomic orbitals and their electrons

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**Quantum Numbers There are 4 types of Quantum Numbers**

Principal – distance from the nucleus Angular Momentum- Orbital Shape Magnetic- Orbital position with respect to the X, Y, & Z axes. Spin- Has only two values (+1/2 or –1/2) and is needed to specify 1 of 2 positional orientations of an electron

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**Principal Quantum Number**

Symbolized by the letter N, indicates the main energy levels surrounding the nucleus There are 7 principal quantum numbers A.K.A. – Shells Value of N is a whole number ex. 1,2,3 ect.. Main Energy Level – N=1; closest to the nucleus or ground state Ground State- state of the lowest energy of the atom. As N increases, the distance from the nucleus increases and the energy increases

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**Angular Momentum Quantum Number**

Indicates the shape of the orbital. Within each main energy level beyond the first, orbitals with different shapes occupy different regions A.K.A. – Sublevels or Subshells The number of sublevels = Value of the Principal Quantum Number

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**Magnetic Quantum Number**

Indicates the orientation of a orbital about the nucleus There are 4 types of orbital orientation S Orbital P Orbital D Orbital F Orbital

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Spin Quantum Number Has only two possible values: +1/2 or –1/2. These values indicate two possible states of an electron in an orbital Spin Quantum # is significant because each single orbital can hold no more than two electrons, which must have opposite spin.

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**S orbitals 1 s orbital for every energy level Spherical shaped**

Each s orbital can hold 2 electrons Called the 1s, 2s, 3s, etc.. orbitals.

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**P orbitals Start at the second energy level 3 different directions**

3 different shapes Each can hold 2 electrons

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P Orbitals

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**D orbitals Start at the third energy level 5 different shapes**

Each can hold 2 electrons

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**F orbitals Start at the fourth energy level**

Have seven different shapes 2 electrons per shape

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F orbitals

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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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By Energy Level Any more than the fourth and not all the orbitals will fill up. You simply run out of electrons The orbitals do not fill up in a neat order. The energy levels overlap Lowest energy fill first.

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**Question for You How many principal quantum numbers are there?**

What is the maximum number of electrons that can fill the 3rd energy level? How many orbitals are in the sublevel F? What is the total number of orbitals for the 3rd main energy level?

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**Electron Configuration**

The way electrons are arranged in atoms There are three rules which help dictate how electrons are arranged in the atoms. Aufbau Principle- electrons occupy the orbitals of the lowest energy first Hund’s Rule- Orbitals of equal energy are each occupied by one electron before any one orbital is occupied by a second electron. All electrons in a single occupied orbital must have the same spin.

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**Electron Configuration cont.**

Pauli Exclusion Principle- No two electrons may occupy any given orbital without having opposite spin. No two electrons in the same atom can have the same set of four quantum numbers. Let’s determine electron configuration. Let’s start with Phosphorus. Need to account for all 15 electrons

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**Electron Configurations**

Distribution of all electrons in an atom Consist of Number denoting the energy level

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**Electron Configurations**

Distribution of all electrons in an atom Consist of Number denoting the energy level Letter denoting the type of orbital

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**Electron Configurations**

Distribution of all electrons in an atom. Consist of Number denoting the energy level. Letter denoting the type of orbital. Superscript denoting the number of electrons in those orbitals.

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**Electron Configurations**

An electron configuration describes the distribution of electrons among the various orbitals in the atom. Electron configuration is represented in two ways. The spdf notation uses numbers to designate a principal shell and letters (s, p, d, f) to identify a subshell; a superscript indicates the number of electrons in a designated subshell.

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**Orbital Diagrams Each box represents one orbital.**

Half-arrows represent the electrons. The direction of the arrow represents the spin of the electron.

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Hund’s Rule “For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”

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**Exceptions to Electron Configuration**

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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 is 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

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**Shortcuts for Electron Configuration**

There are two short handed methods of writing the electron configuration. The 1st method is called the outer-level configuration. That tells you the outer-most configuration for that element. The 2nd method is called the Noble Gas Notation. This tells you the complete notation using Noble Gases. Let’s start with outer-level notation!!!

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**Exceptions to the Aufbau Principle**

Half-filled d subshell plus half-filled s subshell has slightly lower in energy than s2 d4. Filled d subshell plus half-filled s subshell has slightly lower in energy than s2 d9. More exceptions occur farther down the periodic table. They aren’t always predictable, because energy levels get closer together.

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H 1 Li 3 Na 11 K 19 Rb 37 Cs 55 Fr 87 1s1 1s22s1 1s22s22p63s1 1s22s22p63s23p64s1 1s22s22p63s23p64s23d104p65s1 1s22s22p63s23p64s23d104p65s24d10 5p66s1 1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p67s1

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1s2 1s22s22p6 1s22s22p63s23p6 1s22s22p63s23p64s23d104p6 1s22s22p63s23p64s23d104p65s24d105p6 1s22s22p63s23p64s23d104p65s24d10 5p66s24f145d106p6 He 2 Ne 10 Ar 18 Kr 36 Xe 54 Rn 86

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**S- block s1 s2 Alkali metals all end in s1**

Alkaline earth metals all end in s2 really have to include He but it fits better later. He has the properties of the noble gases.

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The P-block p1 p2 p3 p4 p6 p5

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**Transition Metals -d block**

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**F - block f1 f5 f2 f3 f4 f6 f7 f8 f9 f10 f11 f12 f14 f13**

inner transition elements f1 f5 f2 f3 f4 f6 f7 f8 f9 f10 f11 f12 f14 f13

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**Each row (or period) is the energy level for s and p orbitals.**

1 2 3 4 5 6 7 Each row (or period) is the energy level for s and p orbitals.

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**D orbitals fill up after previous energy level so first d is 3d even though it’s in row 4.**

1 2 3 4 5 6 7 3d

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1 2 3 4 5 6 7 4f 5f f orbitals start filling at 4f

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**Summary Outer-Level Configuration**

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**Writing Electron configurations the easy way**

Yes there is a shorthand

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**Electron Configurations repeat**

The shape of the periodic table is a representation of this repetition. When we get to the end of the column the outermost energy level is full. This is the basis for our shorthand.

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**The Shorthand Write the symbol of the noble gas before the element.**

Then the rest of the electrons. Aluminum - full configuration. 1s22s22p63s23p1 Ne is 1s22s22p6 so Al is [Ne] 3s23p1

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**More examples Ge = 1s22s22p63s23p64s23d104p2 Ge = [Ar] 4s23d104p2**

Hf=1s22s22p63s23p64s23d104p65s2 4d105p66s24f145d2 Hf=[Xe]6s24f145d2

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**The Shorthand Again Sn- 50 electrons The noble gas before it is Kr**

Takes care of 36 Next 5s2 Then 4d10 Finally 5p2 [ Kr ] 5s2 4d10 5p2

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Quantum Numbers Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. Each orbital describes a spatial distribution of electron density. An orbital is described by a set of three quantum numbers.

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**The Wave-like Electron**

The electron propagates through space as an energy wave. To understand the atom, one must understand the behavior of electromagnetic waves. Louis deBroglie

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**The Quantum Mechanical Model**

A totally new approach De Broglie said matter could be like a wave. De Broglie said they were like standing waves. The vibrations of a stringed instrument

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What’s possible? You can only have a standing wave if you have complete waves. There are only certain allowed waves. In the atom there are certain allowed waves called electrons. 1925 Erwin Schroedinger described the wave function of the electron Much math, but what is important are the solutions

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**Schrödinger’s Equation**

The wave function is a F(x, y, z) Actually F(r,θ,φ) Solutions to the equation are called orbitals. These are not Bohr orbits. Each solution is tied to a certain energy These are the energy levels Animation

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**What does the wave Function mean?**

nothing. it is not possible to visually map it. The square of the function is the probability of finding an electron near a particular spot. best way to visualize it is by mapping the places where the electron is likely to be found.

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Probability Distance from nucleus

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**Sum of all Probabilities**

Distance from nucleus

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**Defining the size The nodal surface.**

The size that encloses 90% to the total electron probability. NOT at a certain distance, but a most likely distance. For the first solution it is a a sphere.

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Quantum Mechanics Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. It is known as quantum mechanics. © 2009, Prentice-Hall, Inc.

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Quantum Mechanics The wave equation is designated with a lower case Greek psi (). The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time. © 2009, Prentice-Hall, Inc.

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Quantum Numbers Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. Each orbital describes a spatial distribution of electron density. An orbital is described by a set of three quantum numbers. © 2009, Prentice-Hall, Inc.

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**Quantum Numbers There are many solutions to Schrödinger’s equation**

Each solution can be described with quantum numbers that describe some aspect of the solution. Principal quantum number (n) size and energy of an orbital Has integer values >0

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s Orbitals Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron. © 2009, Prentice-Hall, Inc.

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**p Orbitals The value of l for p orbitals is 1.**

They have two lobes with a node between them. © 2009, Prentice-Hall, Inc.

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**d Orbitals The value of l for a d orbital is 2.**

Four of the five d orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center. © 2009, Prentice-Hall, Inc.

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**Quantum numbers Angular momentum quantum number l shape of the orbital**

integer values from 0 to n-1 l = 0 is called s l = 1 is called p l =2 is called d l =3 is called f l =4 is called g

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**Magnetic Quantum Number (ml)**

The magnetic quantum number describes the three-dimensional orientation of the orbital. Allowed values of ml are integers ranging from -l to l: −l ≤ ml ≤ l. Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc. © 2009, Prentice-Hall, Inc.

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**Magnetic Quantum Number (ml)**

Orbitals with the same value of n form a shell. Different orbital types within a shell are subshells. © 2009, Prentice-Hall, Inc.

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Spin Quantum Number, ms This led to a fourth quantum number, the spin quantum number, ms. The spin quantum number has only 2 allowed values: +1/2 and −1/2. © 2009, Prentice-Hall, Inc.

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**Pauli Exclusion Principle**

No two electrons in the same atom can have exactly the same energy. Therefore, no two electrons in the same atom can have identical sets of quantum numbers. © 2009, Prentice-Hall, Inc.

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Quantum Theory and the Electronic Structure of Atoms

Quantum Theory and the Electronic Structure of Atoms

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