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**Electronic Structure of Atoms**

Chapter 6 Electronic Structure of Atoms

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**Lesson 1: The Wave Nature of Light**

Much of our present understanding of our electronic structure of atoms has come from analysis o the light either emitted or absorbed by substances. To understand electronic structure of an atom, we must first learn about light. Made up of electromagnetic radiation. Waves of electric and magnetic fields at right angles to each other.

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**Parts of a wave Wavelength – the distance between**

two adjacent peaks (or troughs) l Frequency = number of cycles in one second Measured in hertz 1 hertz = 1 cycle/second = s-1

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Frequency = n

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**Kinds of EM waves There are many different l and n**

Radio waves, microwaves, x rays and gamma rays are all examples. Light is only the part our eyes can detect. G a m m a R a d i o R a y s w a v e s

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**Electromagnetic Spectrum**

Wavelengths in the spectrum range from very short gamma rays to very long radio waves. Notice that the color of visible light can be expressed quantitatively by wavelength

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**The speed of light in a vacuum is 2.998 x 108 m/s = c c = ln**

What is the wavelength of light with a frequency 5.89 x 105 Hz? What is the frequency of blue light with a wavelength of 484 nm?

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Sample Problems: The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of 589 nm. What is the frequency of this radiation?

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Sample Problem A laser used in eye surgery to fuse detached retinas produces radiation with a wavelength of 640 nm. Calculate the frequency of this radiation.

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Sample Problem An FM radio station broadcasts electromagnetic radiation at a frequency of MHz (megahertz = 106 s-1). Calculate the wavelength of this radiation.

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6.15 a What is the frequency of radiation that has a wavelength of 955 micrometers? (10-6 meters)

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6.15b What is the wavelength of radiation that has a frequency of 5.50 x 1014 s-1?

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**Lesson 2: Quantized Energy and Photons**

Although the wave model of light explains many aspects of its behavior, there are several phenomena this model can’t explain. Blackbody radiation – the emission of light from hot objects. Photoelectric effect – the emission of electrons from metal surfaces on which light shines. Emission spectra – the emission of light from electronically excited gas atoms.

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**Hot Objects and the Quantization of Energy – Blackbody Radiation**

Matter and energy were seen as different from each other in fundamental ways. Matter was particles. Energy could come in waves, with any frequency. Max Planck found that as the cooling of hot objects couldn’t be explained by viewing energy as a wave.

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**Hot Objects and the Quantization of Energy**

Planck found DE came in chunks with size hn DE = nhn where n is an integer. and h is Planck’s constant h = x J-s these packets of hn are called quantum

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**The Photoelectric Effect - Einstein is next**

Light shining on a clean metal surface causes the surface to emit electrons. Said electromagnetic radiation is quantized in particles called photons. Each photon has energy = hn = hc/l Combine this with E = mc2 You get the apparent mass of a photon. m = h / (lc)

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You Try It… Calculate the energy of one photon of yellow light whose wavelength is 589 nm.

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Sample Exercise A laser emits light with a frequency of 4.69 x 1014 s-1. What is the energy of one photon of the radiation from this laser?

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**Sample exercise continued…**

If the laser emits a pulse of energy containing 5.0 x 1017 photons of this radiation, what is the total energy of that pulse?

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**Sample Exercise Continued**

If the laser emits 1.3 x 10-2 Joules of energy during a pulse, how many photons are emitted during the pulse?

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**Which is it? Is energy a wave like light, or a particle?**

Yes It is Both Concept is called the Wave -Particle duality. What about the other way, is matter a wave? Yes

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**Lesson 3: Line Spectra and the Bohr Model (Emission Spectra)**

The work of Planck and Einstein paved the way for understanding how electrons are arranged in atoms. In 1913, the Danish physicist Niels Bohr offered a theoretical explanation of line spectra.

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Additional Examples Calculate the smallest increment of energy that can be emitted or absorbed at a wavelength of 438 nm. Calculate the energy of a photon of frequency of 6.75 x 1012 s-1 What wavelength of radiation has photons of energy 2.87 x Joules? In what portion of the electromagnetic spectrum would this radiation be found?

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Another example Molybdenum metal must absorb radiation with a minimum frequency of 1.09 x 1015 s-1 before it can emit an electron from its surface via the photoelectric effect. What is the minimum energy needed to produce this effect? What wavelength radiation will provide a photon of this energy? If molybdenum is irradiated with light of wavelength of 120 nm, what is the maximum possible kinetic energy of the emitted electrons?

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**Niels Bohr Developed the quantum model of the hydrogen atom.**

He said the atom was like a solar system. The electrons were attracted to the nucleus because of opposite charges. Didn’t fall in to the nucleus because it was moving around.

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The Bohr Ring Atom He didn’t know why but only certain energies were allowed. He called these allowed energies energy levels. Putting Energy into the atom moved the electron away from the nucleus. From ground state to excited state. When it returns to ground state it gives off light of a certain energy.

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The Bohr Ring Atom n = 4 n = 3 n = 2 n = 1

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Give it some thought… As the electron in a hydrogen atom jumps from n=3 orbit to the n=7 orbit, does it absorb energy or emit energy?

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Line Spectra A source of radiant energy may emit a single wavelength, as in the light from a laser. This is known as monochromatic Most common radiation sources, including light bulbs and stars, produce radiation containing many different wavelengths. When this radiation is separated into its different wavelength components, a spectrum is produced.

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**Continuous Spectrum vs. Line Spectrum**

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Continuous Spectrum When a prism spreads light from a light bulb into its component wavelengths, a continuous spectrum is produced. Most familiar example is the rainbow produced when raindrops or mist acts as a prism from sunlight.

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**Line Spectrum Not all radiation sources produce a continuous spectrum.**

When neon gas is placed under pressure in a tube and a high voltage is applied, the gas emits the familiar red-orange glow of many “neon” signs. When light coming from such tubes is passed through a prism, only a few wavelengths are present. The colored lines are separated by black regions which correspond to wavelengths that are absent from the light. A spectrum containing radiation of only specific wavelengths is called a line spectrum.

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Sodium Line Spectrum

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Flame Testing

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Rydberg Equation An equation that allows us to calculate the wavelengths of all the spectral lines present in a line spectrum.

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**Rydberg Equation Lambda is the wavelength of a spectral line.**

RH is the Rydberg constant ( x 107 m-1) n1 and n2 are positive integers, with n2 being larger than n1. These will represent the energy level electrons reside in.

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Energy levels The lowest energy state (n=1) is the energy level closest to the nucleus. It can hold up to 2 electrons. The next lowest energy state (n=2) is the energy level located outside energy level one, and so forth. Ground State – when the electron is found in its lowest energy level possible. Excited State – when the electron has absorbed energy to jump to an outer energy level.

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Sample Exercise Predict which of the following electronic transitions produces the spectral lines having the longest wavelength: n=2 to n=1 n=3 to n = 2 n=4 to n=3

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Sample Exercise Indicate whether each of the following electronic transitions emits energy or requires the absorption of energy A. n=3 to n=1 B. n=2 to n=4

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Example Problem For each of the following electronic transitions in the hydrogen atom, calculate the energy, frequency, and wavelength of the associated radiation, and determine whether the radiation is emitted or absorbed during the transition: From n=4 to n=1 From n=5 to n=2 From n=3 to n=6

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**Lesson 4: Matter as a Wave**

Louis de Broglie proposed that the characteristic wavelength of the electron depends on its mass and on its velocity: Using the velocity v instead of the frequency n we get. de Broglie’s equation l = h/mv Mass x velocity = momentum Note: mass must be expressed in Kg Can calculate the wavelength of an object. The quantity mv for any object is called its momentum De Broglie used the term matter waves.

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You Try It… What is the wavelength of an electron moving with a speed of 5.97 x 106 m/s? The mass of an electron is 9.11 x g.

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Example Use the de Broglie relationship to determine the wavelengths of the following objects: An 85 kg person skiing at 50 km/hour A 10 gram bullet fired at 250 m/s A lithium atom moving at 2.5 x 105 m/s

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