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**Chapter. 5: Electrons in Atoms**

Section 5.1: Light & Quantized Energy Section 5.2: Quantum Theory & the Atom

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**Objectives Identify the inadequacies in the Rutherford atomic model.**

Identify the new assumption in the Bohr model of the atom. Describe the energies and positions of electrons according to the quantum mechanical model. Describe how the shapes of orbitals at different sublevels differ.

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**Recall . . . Rutherford’s nuclear atomic model**

The atom is mostly empty space. All of an atom’s positive charge and almost all of its mass are concentrated in a central structure called the nucleus. Fast-moving electrons are found in the space surrounding the nucleus.

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**Unanswered Questions Rutherford’s atomic model was incomplete.**

Why weren’t the negatively charged electrons pulled into the positively charged nucleus? How were electrons “arranged” around the nucleus? How does the model explain differences in chemical behavior between elements?

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**More Unanswered Questions**

In the early 1900’s, scientists found that certain elements emitted visible light when heated in a flame. Different elements emitted different colors of light. Rutherford’s model could not explain this either! Fluorine Copper

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**The Development of Atomic Models**

In 1913, Neils Bohr (who was working for Rutherford) believed Rutherford’s model needed improvement.

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**Bohr’s model came to be known as the planetary model.**

Bohr’s Atomic Model Bohr proposed that an electron is found only in specific circular paths, or orbits, around the nucleus. Bohr’s model came to be known as the planetary model.

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Bohr’s Atomic Model Each possible electron orbit had a fixed amount of energy that was called the electron’s energy level. The closer the orbit was to the nucleus, the smaller the orbit was AND the lower the electron’s energy level.

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The Planetary Model In Bohr’s model, the lowest allowable energy state is called the ground state. When an atom gains energy, it is said to be in an excited state. Many ”excited” states are possible.

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Bohr’s Atomic Model To become “excited” and move from one energy level to another, an electron had to gain or lose just the right amount of energy. A quantum of energy is the amount of energy required to move an electron from one energy level to another energy level.

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**An Analogy Think of each quantum of energy as a step in a staircase.**

To walk up the staircase, you move up one step at a time. You do not move up a 1/2 step or 1 1/2 steps. When an electron increases in energy, it increases 1 quantum (or 1 energy level) at a time. Quanta 4 3 2 1

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Bohr’s Atomic Model The Bohr model gave results in agreement with experimental data for the hydrogen atom. But it still failed to explain the energies absorbed and emitted by atoms with more than one electron.

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**The Development of Atomic Models**

Erwin Shrödinger ( ) devised and solved a mathematical equation to describe the motion of electrons. The modern description of the electrons in atoms, the quantum mechanical model, comes from the mathematical solutions of Schrödinger’s equation.

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**The Quantum Mechanical Model**

The energy levels of electrons in the quantum mechanical model are labeled by principal quantum numbers (n). These are assigned the values n=1,2,3,4,5,6…

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**The Quantum Mechanical Model**

An electron’s path around the nucleus is not circular but is described in terms of probability. The probability of finding an electron in various locations around the nucleus can be pictured in terms of a blurry cloud of negative charge. The Schrodinger wave equation is too complex to be considered here, however each solution to the equation is known as a wave function. The wave function is related to the probability of finding the electron within a particular volume of space around the nucleus

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**Quantum Mechanical Model**

The cloud is most dense where the probability of finding the electron is highest. An imaginary boundary of the “electron cloud” encloses the area that has a 90% probability of containing electrons. The probability of finding electrons in certain regions of an atom is described by orbitals.

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**Quantum Mechanical Model**

Because electrons have different energies, they are found in different probable locations around the nucleus. An atomic orbital is a 3-d region around the nucleus of an atom where an electron with a given energy is likely to be found. For each principal energy level, there are several orbitals with different shapes, sizes, and energies.

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**Quantum Mechanical Model**

Each principal energy level consists of one or more sublevels . . . As n increases, the # of sublevels increases as does their distance from the nucleus. Just like your home address consists of a state, a city and a street name within the city, the “address” of an electron consists of its principal energy level, its sublevel and its orbital within that sublevel.

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**Quantum Mechanical Model**

Sublevels are labeled s, p, d, or f, according to the shapes of their orbitals. For n=1, there is one sublevel. It is called “s”. For n=2, there are 2 sublevels. They are called “s” and “p”. For n=3, there are 3 sublevels. They are called ? Just as proposed in the Bohr model, the energy of the electron increases as n increases. Unlike the Bohr model, however, each principal energy level is divided into one or more sublevels. The number of sublevels in each principal energy = the quantum number n for that energy level. There is one sublevel when n=1, two sublevels when n=2 and so on. These sublevels are labeled with a number that is the value of the quantum number n and a letter (s, p, d or f) that corresponds to the type of sublevel. As we go on keep in mind the definition of an orbital – region in which an electron with a particular energy is likely to be found.

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**Quantum Mechanical Model**

Each type of sublevel consists of one or more orbitals. There is 1 “s” orbital There are 3 “p” orbitals There are 5 “d” orbitals There are 7 “f” orbitals

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**Quantum Mechanical Model**

All s orbitals are spherical. Each energy level has a “s” orbital. They will differ in size.

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**Atomic Orbitals “p” orbitals have a dumbbell shape.**

There are 3 “p” orbitals in each energy level that contains “p” orbitals. This is because there are 3 orientations that the “p” orbital can have in space.

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Atomic Orbitals “d” and “f” orbitals have very complex shapes with many different orientations. There are 5 possible “d” orbitals and “7” possible “f” orbitals.

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**Quantum Mechanical Model**

Review The principal energy level or principal quantum number is designated by n. The number of sublevels in a principal energy level is always equals the quantum number n. Sublevels have letter designations (s, p, d, or f), depending on the shapes of the orbitals found there.

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Review of Sublevels The lowest principal energy level (n=1) has 1 sublevel and it is called 1s. The second principal energy level (n=2) has 2 sublevels, 2s and 2p. The 2p sublevel is of higher energy than the 2s. 2p consists of 3 “p” orbitals of equal energy. The 2nd principal energy level, therefore, has 4 orbitals, 1 2s and 3 2p’s.

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Review of Sublevels The third principal energy level (n=3) has 3 sublevels - 3s, 3p, and 3d. The 3d orbitals are of higher energy than the 3p. 3d consists of 5 equal energy orbitals. The 3rd principal energy level, therefore, has a total of 9 orbitals (1 3s, 3 3p’s, and 5 3d’s)

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Review of Sublevels The fourth principal energy level (n=4) has 4 sublevels - 4s, 4p, 4d, and 4f. The 4f orbitals are of higher energy than the 4d. 4f consists of 7 equal energy orbitals. The 4th principal energy level, therefore, has a total of 16 orbitals (1 4s, 3 4p’s, 5 4d’s and 7 4f’s).

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Orbitals and Energy An “orbital diagram”

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**Quantum Mechanical Model**

The number of sublevels always equals the quantum number n. The number of orbitals in each sublevel is always an odd number: s has 1 orbital; p has 3 orbitals; d has 5 orbitals; f has 7 orbitals. The total number of orbitals in each energy level = n2 (In n= 3, there are 9 orbitals: 1 s, 3 p’s , and 5 d’s.) Each orbital may contain at most 2 electrons. Therefore, the maximum number of electrons in each energy level = 2n2.

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**Maximum Electron Numbers for Principal**

Orbitals and Energy Maximum Electron Numbers for Principal Energy Level n Max. # of electrons 1 2 8 3 18 4 32

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