# 1 © 2009 Brooks/Cole - Cengage ATOMIC STRUCTURE. 2 © 2009 Brooks/Cole - Cengage Atomic Structure Much of what we know about the very nature of matter.

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1 © 2009 Brooks/Cole - Cengage ATOMIC STRUCTURE

2 © 2009 Brooks/Cole - Cengage Atomic Structure Much of what we know about the very nature of matter and the universe around us is due to the work of pioneering chemists, mathematicians and physicists in the late 19 th and early 20 th centuriesMuch of what we know about the very nature of matter and the universe around us is due to the work of pioneering chemists, mathematicians and physicists in the late 19 th and early 20 th centuries »No Computers, calculators, Starbucks, cell phones or even ELECTRICITY This knowledge sprang from studies on lightThis knowledge sprang from studies on light »What is it? »How do atoms interact with it? »How is it made?

3 © 2009 Brooks/Cole - Cengage Electromagnetic Radiation In 1864 (what was going on in America at the time?), James Maxwell developed a mathematical way to describe radiationIn 1864 (what was going on in America at the time?), James Maxwell developed a mathematical way to describe radiation He said that radiation is a wave with electric and magnetic fields at right angles to each other move togetherHe said that radiation is a wave with electric and magnetic fields at right angles to each other move together Since it is a wave, it has the following characteristics of all wavesSince it is a wave, it has the following characteristics of all waves –Wavelength: λ (lambda) = The distance between successive crests of a wave. It is measured in units of distance (nanometers, micrometers, meters) –Frequency: ν (nu) = The number of waves that pass a given point in some amount of time (usually per second). It is measured in Hertz (Hz) or s -1 The speed of an electromagnetic wave is defined as:The speed of an electromagnetic wave is defined as: c = λν c = λν where c is the Universal Constant = 3.00 x10 8 m/s

6 © 2009 Brooks/Cole - Cengage Long wavelength, small frequency v Short wavelength, high frequency v increasing frequency increasing wavelength Electromagnetic Radiation

7 © 2009 Brooks/Cole - Cengage Red light has = 700 nm. Calculate the frequency. Electromagnetic Radiation

8 © 2009 Brooks/Cole - Cengage Long wavelength Long wavelength small frequency small frequency low energy Short wavelength Short wavelength high frequency high frequency high energy Electromagnetic Radiation

9 © 2009 Brooks/Cole - Cengage Electromagnetic Spectrum

10 © 2009 Brooks/Cole - Cengage Let’s look at an object being heated The emitted light from a heated object comes from a collection of oscillatorsThe emitted light from a heated object comes from a collection of oscillators –Some at high energy, some at intermediate energy, some at low energy In 1879, Josef Stefan determined that the total intensity of all radiation emitted from a heated object increases as the fourth power of temperatureIn 1879, Josef Stefan determined that the total intensity of all radiation emitted from a heated object increases as the fourth power of temperature –Intensity=(5.67x10 -8 Wm -2 K -4 ) · T 4 »1 Watt (W) = 1J/sec

11 © 2009 Brooks/Cole - Cengage Wien’s Law Wilhelm Wien studied the relationship between temperature and the wavelength of maximum intensity in a black body emitter. He found that as Temperature INCREASES, the wavelength of maximum emission DECREASES We can summarize this in Wien’s Law: T max = Constant = 2.9 Kmm

12 © 2009 Brooks/Cole - Cengage Quantization of Energy (Planck and Einstein) For centuries people have observed that as you heat an object, it goes from red to orange-yellow to whiteFor centuries people have observed that as you heat an object, it goes from red to orange-yellow to white –The phrase “white hot” comes from this What are we actually observing?What are we actually observing? This emitted light is an indicator of the heat given off by the objectThis emitted light is an indicator of the heat given off by the object The problem scientists in the 1800’s had was that it was theorized that the more heat you put into an object, the higher the intensity of radiation that would be emitted at decreasing wavelengthThe problem scientists in the 1800’s had was that it was theorized that the more heat you put into an object, the higher the intensity of radiation that would be emitted at decreasing wavelength “The Ultraviolet Catastrophe”

13 © 2009 Brooks/Cole - Cengage The Ultraviolet Catastrophe According to Classical Physics at the time, having a cookout should turn into a nightmare. The grill should be emitting x-ray and gamma ray radiation But we know this doesn’t happen. Max Planck studied this and found…

14 © 2009 Brooks/Cole - Cengage Quantization of Energy See Chem & Chem Reactivity, Figure 6.3 Planck deduced that energy would be quantized and this explained the “Catastrophe”Planck deduced that energy would be quantized and this explained the “Catastrophe” With quantization, only radiation of certain energies would be emittedWith quantization, only radiation of certain energies would be emitted

15 © 2009 Brooks/Cole - Cengage E = h · E = h · Quantization of Energy Energy of radiation is proportional to frequency h = Planck’s constant = 6.6262 x 10 -34 J·s An object can gain or lose energy by absorbing or emitting radiant energy in QUANTA.

16 © 2009 Brooks/Cole - Cengage Light with a short (large ) has a large E. Light with large (small ) has a small E. E = h · E = h · Quantization of Energy

17 © 2009 Brooks/Cole - Cengage Let’s look at an object being heated As we heat a metal bar, the atoms in the bar vibrate fasterAs we heat a metal bar, the atoms in the bar vibrate faster The atoms are called oscillatorsThe atoms are called oscillators As they drop back down to a lower vibrational state they emit some radiationAs they drop back down to a lower vibrational state they emit some radiation Each oscillator has a fundamental frequency and the energy of the emitted radiation is a multiple of this frequency (this is where n comes into play)Each oscillator has a fundamental frequency and the energy of the emitted radiation is a multiple of this frequency (this is where n comes into play) For a single energy level change, the equation becomes:For a single energy level change, the equation becomes: E=hν(Planck’s Equation)

18 © 2009 Brooks/Cole - Cengage Energy of Radiation Energy of 1.00 mol of photons of red light. E = h· E = h· = (6.63 x 10 -34 J·s)(4.29 x 10 14 s -1 ) = (6.63 x 10 -34 J·s)(4.29 x 10 14 s -1 ) = 2.85 x 10 -19 J per photon = 2.85 x 10 -19 J per photon E per mol = (2.85 x 10 -19 J/ph)(6.02 x 10 23 ph/mol) (2.85 x 10 -19 J/ph)(6.02 x 10 23 ph/mol) = 172 kJ/mol = 172 kJ/mol

19 © 2009 Brooks/Cole - Cengage Photoelectric Effect Experiment demonstrates the particle nature of light.

20 © 2009 Brooks/Cole - Cengage Photoelectric Effect Classical theory said that E of ejected electron should increase with increase in light intensity—not observed! No e - observed until light of a certain minimum E (or frequency, remember Placnk’s equation?) is used.No e - observed until light of a certain minimum E (or frequency, remember Placnk’s equation?) is used. –Once this value is reached, electrons are immediately ejected Number of e - ejected depends on light intensity.Number of e - ejected depends on light intensity. The kinetic energy of the ejected electrons increases with the frequency of the incident radiationThe kinetic energy of the ejected electrons increases with the frequency of the incident radiation A. Einstein (1879- 1955)

21 © 2009 Brooks/Cole - Cengage Photoelectric Effect Understand experimental observations if light consists of particles called PHOTONS of discrete energy.

22 © 2009 Brooks/Cole - Cengage Photoelectric Effect Einstein explained the observations of photo-electric experiments by combining Planck’s equation with a new conceptEinstein explained the observations of photo-electric experiments by combining Planck’s equation with a new concept –Light has particle-like properties –Massless packets of energy are called PHOTONS (hv) and the energy of the packets is proportional to their frequency No electrons are ejected by the metal if the incident photons do not have a high enough energyNo electrons are ejected by the metal if the incident photons do not have a high enough energy If the frequency is high enough, the energy is high enough and an electron is knocked offIf the frequency is high enough, the energy is high enough and an electron is knocked off A. Einstein (1879- 1955)

23 © 2009 Brooks/Cole - Cengage Photoelectric Effect Let’s look at this in more detail: If we have a stream of photons colliding with a metal object, some of those photons are going to collide with the electrons in the metal The photons have an energy associated with them (hv) but this value must be above a certain minimum to eject an electron from the metal. Different metals do not release electrons with the exact same incident photons The metals want to hold onto the electrons and have a characteristic energy value associated with them called a WORK FUNCTION,  If the energy of the incident photons is greater than , then the metal releases electrons 1/2m e v 2 = hv -  E k of ejected electron Work function of metal Energy of incident photon

24 © 2009 Brooks/Cole - Cengage Atomic Line Emission Spectra and Niels Bohr It has long been known that applying high voltage to a tube containing a gas would result in the gas giving off lightIt has long been known that applying high voltage to a tube containing a gas would result in the gas giving off light However, if we split the light into its component wavelengths with a prism, we’ll see a small number of lines at specific colors (wavelengths)However, if we split the light into its component wavelengths with a prism, we’ll see a small number of lines at specific colors (wavelengths)

25 © 2009 Brooks/Cole - Cengage Line Emission Spectra of Excited Atoms Excited atoms emit light of only certain wavelengths The wavelengths of emitted light depend on the element.

26 © 2009 Brooks/Cole - Cengage Visible lines in H atom spectrum are called the BALMER series. High E Short Short High High Low E Long Long Low Low Line Emission Spectra of Excited Atoms

27 © 2009 Brooks/Cole - Cengage Line Spectra of Other Elements Why do elements emit at certain characteristic wavelengths? Balmer and Rydberg developed an explanation for the line emission behaviour (Rydberg Formula) R = Rydberg Constant = 1.0974x10 -3 m -1

28 © 2009 Brooks/Cole - Cengage Line Spectra R = Rydberg Constant = 1.0974x10 -3 m -1 When n 1 =2 (and n 2 =2, 3, 4…) You can calculate the Balmer Series of lines When n 1 =1 (and n 2 =2, 3, 4…) You can calculate the Lyman Series of lines

29 © 2009 Brooks/Cole - Cengage What do Line Spectra Tell Us? The characteristic line spectra of each element tells us that electrons can only have certain SPECIFIC energies (that’s what those n values mean, but more on that in a minute) Each element has a unique configuration of electrons as evidenced by their unique line spectra

30 © 2009 Brooks/Cole - Cengage Atomic Spectra and Bohr 1.Any orbit should be possible and so is any energy. 2.But a charged particle moving in an electric field should emit energy. End result should be destruction! One view of atomic structure in early 20th century was that an electron (e-) traveled about the nucleus in an orbit.

31 © 2009 Brooks/Cole - Cengage Atomic Spectra and Bohr Bohr said classical view is wrong. Need a new theory — now called QUANTUM or WAVE MECHANICS. e- can only exist in certain discrete orbits — called stationary states. e- is restricted to QUANTIZED energy states. Energy of state = - Rhc/n 2 where n = quantum no. = 1, 2, 3, 4,....

32 © 2009 Brooks/Cole - Cengage Atomic Spectra and Bohr Only orbits where n = some positive integer are permitted.Only orbits where n = some positive integer are permitted. The energy of an electron in an orbit has a negative valueThe energy of an electron in an orbit has a negative value An atom with its electrons in the lowest possible energy level is at GROUND STATEAn atom with its electrons in the lowest possible energy level is at GROUND STATE Energy of quantized state = - Rhc/n 2

33 © 2009 Brooks/Cole - Cengage Atomic Spectra and Bohr If e-’s are in quantized energy states, then ∆E of states can have only certain values. This explain sharp line spectra. PLAY MOVIE

35 © 2009 Brooks/Cole - Cengage Origin of Line Spectra Balmer series

36 © 2009 Brooks/Cole - Cengage Atomic Line Spectra and Niels Bohr Bohr’s theory was a great accomplishment. Rec’d Nobel Prize, 1922 Problems with theory — theory only successful for H.theory only successful for H. introduced quantum idea artificially.introduced quantum idea artificially. So, we go on to QUANTUM or WAVE MECHANICSSo, we go on to QUANTUM or WAVE MECHANICS Niels Bohr (1885-1962)

37 © 2009 Brooks/Cole - Cengage Wave-Particle Duality de Broglie (1924) proposed that all moving objects have wave properties. For light: E = mc 2 E = h = hc / E = h = hc / Therefore, mc = h / Therefore, mc = h / and for particles (mass)(velocity) = h / (mass)(velocity) = h / de Broglie (1924) proposed that all moving objects have wave properties. For light: E = mc 2 E = h = hc / E = h = hc / Therefore, mc = h / Therefore, mc = h / and for particles (mass)(velocity) = h / (mass)(velocity) = h / L. de Broglie (1892-1987)

38 © 2009 Brooks/Cole - Cengage Baseball (115 g) at 100 mph = 1.3 x 10 -32 cm = 1.3 x 10 -32 cm e- with velocity = 1.9 x 10 8 cm/sec = 0.388 nm = 0.388 nm Experimental proof of wave properties of electrons Wave-Particle Duality The mass times the velocity of the ball is very large, so the wavelength is very small for the baseballThe mass times the velocity of the ball is very large, so the wavelength is very small for the baseball The deBroglie equation is only useful for particles of very small massThe deBroglie equation is only useful for particles of very small mass

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