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Chapter 4-2 The Quantum Model of the Atom Coach Kelsoe Chemistry Pages 104–110

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Electrons as Waves Investigations into the photoelectric effect and hydrogen atomic emission showed that light behaves as a wave and as a particle. Louis de Broglie asked if electrons could behave the same way as light. Broglie suggested that electrons be considered waves confined to the space around the atomic nucleus. It turns out that electrons do have wavelike properties.

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Properties of Electrons Scientists demonstrated that electrons can be diffracted and can interfere with each other. Diffraction is the bending of a wave as it passes by the edge of an object. Interference occurs when waves overlap, which results in the reduction of energy in some areas and an increase in others.

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Heisenberg Uncertainty Principle The idea that electrons have a wave-particle nature bothered scientists. Werner Heisenberg proposed an idea that involved the detection of electrons. The Heisenberg uncertainty principle states that it is impossible to determine simultaneously both the position and velocity of an electron or any other particle.

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The Schrödinger Wave Equation In 1926, Erwin Schrödinger used the idea that electrons act like waves and particles to develop an equation that treated electrons as waves. His equation along with the Heisenberg uncertainty principle laid the foundation for the modern quantum theory. Quantum theory describes mathematically the wave properties of electrons and other very small particles.

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Orbits or Orbitals? Electrons do not travel in neat orbits around the nucleus like Bohr said. Electrons exist in regions called orbitals, three- dimensional regions around the nucleus that indicate the probable location of an electron. Orbitals have different sizes and shapes.

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Atomic Orbitals In Bohr’s atomic model, electrons of increasing energy occupy orbits farther from the nucleus. In Schrödinger’s equation, an electron’s energy is not the only characteristic of an orbital. In order to completely describe orbitals, scientists use quantum numbers.

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Warning! The next nine slides may be hazardous to your science health. Don’t concentrate too much on the lingo. The concepts will hit you soon. Hang tight and understanding will come!

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Quantum Numbers Quantum numbers specify the properties of atomic orbitals and the properties of electrons in orbitals. The first three quantum numbers indicate the main energy level, the shape, and the orientation of an orbital. The fourth describes a fundamental state of the electron that occupies the orbital.

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Principal Quantum Number The principal quantum number, symbolized by n, indicates the main energy level occupied by the electron. Values of n are positive integers only. As n increases, the electron’s energy and its average distance from the nucleus increase. For example, an electron for which n=1 occupies the first, or lowest, main energy level and is located closest to the nucleus.

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Principal Quantum Numbers More than one electron can have the same n value. These are said to be in the same electron shell or energy level. The total number of orbitals that exist in a given energy level is equal to n 2.

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Angular Momentum Quantum Number Except at the first main energy level, orbitals of different shapes exist for a given value of n. The angular momentum quantum number, symbolized by l, indicates the shape of the orbital. The number of orbital shapes possible is equal to n. The values of l allowed are zero and all positive integers less than or equal to n-1.

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Angular Momentum Quantum Number For example, orbitals for which n=2 can have one or two shapes corresponding to l=0 and l=1 Depending on its value of l, an orbital is assigned a letter. lLetter 0s 1p 2d 3f

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Angular Momentum Quantum Number s orbitals are round, p are shaped like 2 teardrops, and d orbitals are more complex. So in the first energy level (n=1), there is only one orbital possible – an s orbital. In the second energy level (n=2), there are two possible orbitals – s and p orbitals.

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Angular Momentum Quantum Number Each atomic orbital is designated by the principal quantum number followed by the letter of the sublevel.

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Magnetic Quantum Number Atomic orbitals can have the same shape but different orientations. The magnetic quantum number, symbolized by m, indicates the orientation of an orbital around the nucleus. Because the s orbital is spherical and is centered around the nucleus, it has only one orientation. The possible orientations are aligned along the x, y, or z axis

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Spin Quantum Number An electron in an orbital can be thought of as spinning on an internal axis. Electrons spin in one of two possible directions. The spin quantum number has only two possible values, which indicate the two fundamental spin states of an electron in an orbital. A single orbital can hold a maximum of two electrons, which must have opposite spins.

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Congratulations! You made it through the rough stuff! The next table will help clarify everything covered in the last nine sides. KNOW THE TABLE!

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Quantum Number Relationships in Atomic Structure Principle Quantum Number (n) Orbitals in Main Energy Level (n orbitals) #Orbitals per Sublevel # Orbitals per Main Energy Level (n 2 ) # Electrons per Orbital # Electrons per Main Energy Level (2n 2 ) 1s1122 2spsp 1313 42626 8 3 spdspd 135135 9 2 6 10 18 4 spdfspdf 13571357 16 2 6 10 14 32

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