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Chapter 7 Quantum Theory of the Atom. What are the electrons doing in the atom?. Why do atoms form ions and molecules?. Why do hydrogen and oxygen “stick” together to form water?. To understand these questions, we need to understand the electronic structure of the atom.

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Chapter 7 quantum theory of the atom l.jpg
Chapter 7Quantum Theory of the Atom


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What are the electrons doing in the atom?

Why do atoms form ions and molecules?

Why do hydrogen and oxygen “stick” together to

form water?

To understand these questions, we need to understand

the electronic structure of the atom

Electronic structure refers to the way the electrons

are arranged in an atom

Copyright © Houghton Mifflin Company. All rights reserved.


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Contents and Concepts

  • Light Waves, Photons, and the Bohr Theory

  • To understand the formation of chemical bonds, you need to know something about the electronic structure of atoms. Because light gives us information about this structure, we begin by discussing the nature of light. Then we look at the Bohr theory of the simplest atom, hydrogen.

  • The Wave Nature of Light

  • Quantum Effects and Photons

  • The Bohr Theory of the Hydrogen Atom


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  • Quantum Mechanics and Quantum Numbers

  • The Bohr theory firmly establishes the concept of energy levels but fails to account for the details of atomic structure. Here we discuss some basic notions of quantum mechanics, which is the theory currently applied to extremely small particles, such as electrons in atoms.

  • Quantum Mechanics

  • Quantum Numbers and Atomic Orbitals


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  • A wave is a continuously repeating change or oscillation in matter or in a physical field.

  • Light is an electromagnetic wave, consisting of oscillations in electric and magnetic fields traveling through space.


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l

l

l

l is thedistance between any two adjacent identical

points of a wave

Copyright © Houghton Mifflin Company. All rights reserved.


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  • Frequency, symbolized by the Greek letter nu, n, is the number of wavelengths that pass a fixed point in one unit of time (usually a second). The unit is 1/S or s-1, which is also called the Hertz (Hz).


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When the wavelength is reduced by a factor of two, the frequency increases by a factor of two.


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c = nl so

l = c/n

n = 6.4 × 1014/s

c = 3.00 × 108 m/s

l = 4.7 × 10-7 m


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c = nl so

n = c/l

l = 681 nm = 6.81 × 10-7 m

c = 3.00 × 108 m/s

l = 4.41 × 1014 /s


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  • One property of waves is that they can be diffracted radiation is called the electromagnetic spectrum.—that is, they spread out when they encounter an obstacle about the size of the wavelength.

  • In 1801, Thomas Young, a British physicist, showed that light could be diffracted. By the early 1900s, the wave theory of light was well established.


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  • The blue Neither understanding is sufficient alone. This is called the –green line of the hydrogen atom spectrum has a wavelength of 486 nm. What is the energy of a photon of this light?

E = hn and

c = nl so

E = hc/l

l = 4.86 nm = 4.86 × 10-7 m

c = 3.00 × 108 m/s

h = 6.63 × 10-34 J  s

l = 4.09 × 10-19 J


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  • In the early 1900s, the atom was understood to consist of a positive nucleus around which electrons move (Rutherford’s model).

  • This explanation left a theoretical dilemma: According to the physics of the time, an electrically charged particle circling a center would continually lose energy as electromagnetic radiation. But this is not the case—atoms are stable.


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  • In addition, this understanding could not explain the observation of line spectra of atoms.

  • A continuous spectrum contains all wavelengths of light.

  • A line spectrum shows only certain colors or specific wavelengths of light. When atoms are heated, they emit light. This process produces a line spectrum that is specific to that atom. The emission spectra of six elements are shown on the next slide.


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  • Energy-Level Postulate to account for

  • An electron can have only certain energy values, called energy levels. Energy levels are quantized.

  • For an electron in a hydrogen atom, the energy is given by the following equation:

  • RH = 2.179 x 10-18 J

  • n = principal quantum number


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  • Transitions Between Energy Levels to account for

  • An electron can change energy levels by absorbing energy to move to a higher energy level or by emitting energy to move to a lower energy level.


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RH = 2.179 × 10-18 J, Rydberg constant


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  • Light is absorbed by an atom when the electron transition is from lower n to higher n (nf > ni). In this case, DE will be positive.

  • Light is emitted from an atom when the electron transition is from higher n to lower n (nf < ni). In this case, DE will be negative.

  • An electron is ejected when nf = ∞.




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ni = 6

nf = 3

RH = 2.179 × 10-18 J

= -1.816 x 10-19 J

1.094 × 10-6 m


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n electron in a hydrogen atom undergoes a transition from = 3

n = 2

n = 1

  • The red line corresponds to the smaller energy difference in going from n = 3 to n = 2. The blue line corresponds to the larger energy difference in going from n = 2 to n = 1.

A minimum of three energy levels are required.


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  • Planck electron in a hydrogen atom undergoes a transition from

  • Vibrating atoms have only certain energies:

    E = hn or 2hn or 3hn

  • Einstein

  • Energy is quantized in particles called photons:

    E = hn

  • Bohr

  • Electrons in atoms can have only certain values of energy. For hydrogen: