 # 1 Atomic Structure chapter 6 written by JoAnne L. Swanson University of Central Florida.

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1 Atomic Structure chapter 6 written by JoAnne L. Swanson University of Central Florida

2 ________________________ The properties of light, the way that energy travels through space, are referred to as __________________________________________________ ______________ Light has properties of both matter and waves. It is described as particles that travel through space in waves. These particles of light are called ______________. Light has 3 main characteristics. These are ____________,  ___________,  and _________, c. Definitions follow:

3 WAVELENGTH –  The distance between two, consecutive, corresponding points on a wave. The units are:_____________ ____________________________________________ FREQUENCY –  – The number of waves that pass a given point per second. The units for frequency are s -1 or Hz. SPEED OF LIGHT – c – The speed of light (measured in a vacuum to negate the effect of friction) is 2.998 x 10 8 m/s.

4 RELATIONSHIPS BETWEEN  and c : Small wavelengthlarge wavelength A small wavelength will have a ______________ than a large wavelength because more waves can pass a given point per second. THEREFORE, WAVELENGTH AND FREQUENCY ARE INVERSELY PROPORTIONAL. A small wavelength also has _________________. THEREFORE, WAVELENGTH AND ENERGY ARE INVERSELY PROPORTIONAL AND ENERGY AND FREQUENCY ARE DIRECTLY PROPORTIONAL.

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6 There were some phenomena that could not be explained by assuming light had only wave properties: Black body radiation Photo electric effect Emission spectra from excited atoms

7 Black body radiation – _______________________________ The higher the temperature, the more intense the glow and the glow can be different colors (or wavelengths) Physicists tried to explain the relationship of the wavelengths of light (color) to the intensity of the heat. Max Planck made the assumption that the atoms were giving off and absorbing heat ___________________ (he called __________). His equation shows the relationship of this fixed amount of energy being proportional to the frequency of the radiation. Multiplying the frequency by a proportionality constant (called Planck’s constant), gives the equation; E = h. Where h=6.63 x 10 -34 Js

8 In Summary - Planck: energy can only be absorbed or released from atoms in certain amounts called quanta. The relationship between energy and frequency is E = h where h is Planck’s constant (6.626  10 -34 J.s).

9 light can strike the surface of some metals and ________________________________ Albert Einstein explained this effect –1921 Nobel Prize in Physics –light has particle-like behavior Photoelectric Effect

10 The Photoelectric Effect and Photons The photoelectric effect provides evidence for the particle nature of light -- “quantization”. If light shines on the surface of a metal, there is a point at which electrons are ejected from the metal. The electrons will only be ejected when ___________ _______________________________________ Below that frequency, _______________________. Above that frequency, the number of electrons ejected depend on the intensity of the light.

11 The Photoelectric Effect and Photons Einstein assumed that light traveled in energy packets called photons. The energy of one photon: E = h

12 Emission Spectra of Excited Atoms Radiation composed of only one wavelength is called _______________. Radiation that spans a whole array of different wavelengths is called ______________. White light can be separated into a continuous spectrum of colors. Note that there are no dark spots on the continuous spectrum. That would correspond to different lines. When atoms are excited by electricity or heat, they emit only _________________________ (that is, not a continuous spectra of light).

13 Modern atomic theory arose out of studies of the interaction of radiation with matter. Electromagnetic waves have characteristic wavelengths and frequencies. Example: visible radiation has wavelengths between ____________________________________.

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15 Neils Bohr, a Danish physicist, assumed the electrons orbited the nucleus analogous to _________ _________________________________________. However, a charged particle moving in a circular path should lose energy. This means that the atom should be unstable and get pulled into the nucleus according to Bohr’s theory. Bohr noted the line spectra of certain elements and _____________________________________________ ______________________. These were called orbits.

16 emission spectrum –____________________________ –______________________________ –___________________________ –emission or bright line spectrum

17 Bohr theorized why excited Hydrogen atoms emitted line spectra. Electrons have energies _______________________________ ___________________________________________________ They will not lose energy in this allowed energy state (orbit). Energy is only emitted or absorbed when an ______________ ____________________. (like one step on a ladder to another). The lowest energy state, n=1, is the _________, like the bottom rung of a ladder and the higher energy states from n=2 and greater are the _______________.

18 Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra. Bohr showed that (equation goes here) where n is the principal quantum number (i.e., n = 1, 2, 3,…). 2.18 x 10 –18 is the ground state energy for H. _____________________________________________________ _______________________________________________

19 Balmer: discovered that the wavelengths in the visible line spectrum of hydrogen fit a simple equation. The Rydberg equation generalizes Balmer’s equation to(equation goes here) where R H is the Rydberg constant (1.096776  10 7 m -1 ), h is Planck’s constant (6.626  10 -34 J·s), n 1 and n 2 are integers (n 2 > n 1 ).

20 Bohr Model The first orbit in the Bohr model has n = 1, is ________ ___________________. The furthest orbit in the Bohr model has n close to infinity and corresponds to zero energy. Electrons in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (h ). The amount of energy absorbed or emitted on movement between states is given by(equation goes here)

21 The change in energy between orbits correspond to: (eq. goes here) When n i > n f, energy is emitted. When n f > n i, energy is absorbed PLEASE SEE PAGE 208-209 IN YOUR TEXT FOR DERIVATIONS OF THESE EQUATAIONS.

22 Limitations of the Bohr Model Can only explain the line spectrum of _________ ________________________. considers only the particle nature of the electron. ___________________________. Electrons travel in circular paths like planets

23 P+P+P+P+ n e–e–e–e– e–e–e–e– e–e–e–e– e–e–e–e– e–e–e–e– e–e–e–e– e–e–e–e– Bohr Model

24 light has a particle nature, matter has a wave nature. Using Einstein’s and Planck’s equations, de Broglie showed:  h / mv (v = velocity) The momentum, mv, is a particle property, whereas ____________________. de Broglie summarized the concepts of waves and particles, with noticeable effects if the objects are small.

25 To determine the mass of a photon of light: derivation - If E=h and c= Then E=hc/ and if E=mc 2 Then m=E/c 2 and so m = hc / c 2 = h / c = h / 2 so, m = h / c and m = h / 2  If the particle is not moving at the speed of light but instead at some velocity, v, m = h / v (where v = velocity) de Broglie’s equation shows the dual nature of light, in that it allows the wavelength of a particle to be calculated.  h / mv

26 EINSTEIN, PLANCK, AND DE BROGLIE’S EXPERIMENTS CONCLUDED THAT MATTER AND ENERGY ARE NOT DISTINCT. MATTER EXHIBITS BOTH PARTICULATE AND WAVE PROPERTIES. ____________ _____________________________________

27 The Uncertainty Principle Heisenberg’s Uncertainty Principle: For electrons: we cannot determine their momentum and position simultaneously.

28 Some important mathematical relationships: c =  E  h Max Planck’s equation showing energy is quantized E = m c 2 Einstein’s theory of relativity, shows energy has mass E  h c  h / mv  de Broglie’s relationship of matter with wavelength c = 2.998 x 10 8 m/s (speed of light in vacuum) ‘h’ is Plank’s constant. h=6.626 x 10 -34 Js or kg m 2 /s Units of ‘E’ are Joules which equal, (kg m 2 / s 2 ) J=kg m 2 / s 2

29  THER EQUATIONS TO KNOW: (derived from Bohr’s model for the hydrogen atom.) E = -2.178 x 10 -18 J (z 2 / n 2 ) where z is the nuclear charge,and for H = +1, and n is the energy level. Ground state, n = 1. Ionized e -, n = infinity and –2.178 x 10 -18 is the ground state energy for H. So, since z 2 =1 for H, then E = -2.178 x 10 -18 J / n 2 for the energy levels available in the H atom And…….. Calculating Energy Difference Between 2 Levels  E = E final - E initial = E hi – E low = h c / So,  E = -2.178 x 10 -18 J / n 2 final – (-2.178 x 10 -18 J /n 2 initial ) = hc /

30 Examples: The color of Sodium atoms, when excited by a flame, are yellow and have the wavelength = 589.0 nm. Calculate a. the frequency of this wavelength and b. the energy associated with this photon? a.  c = 2.998 x 10 8 m/s = 5.090 x 10 14 s -1  x   m b. E  h  6.626 x 10 -34 Js x 5.090 x 10 14 s -1 = 3.37 x 10 -19 J for this photon

31 example: It takes 382 kJ of energy to remove one mole of electrons from gaseous cesium. What is the wavelength associated with this energy? To convert between energy and wavelength, requires the energy to be per photon, not moles of photons, therefore, 382 kJ 382 kJ x 1 mol______ = 6.343 x 10 -19 J (per photon) 1 mol 6.02 x 10 23 photons E  h c so,  hc  E  x 10 -34 Js x 2.998 x 10 8 m/s = 3.13 x 10 -7 m 6.343 x 10 -19 J

32 example: What is the wavelength of an electron with mass = 9.11 x 10 -31 kg, traveling at 5.31 x 10 6 m/s ? m = h / v therefore,  h / m v = 6.626 x 10 -34 Js = 6.626 x 10 -34 kg m 2 s -1 9.11 x 10 -31 kg (5.31 x 10 6 m/s) 4.837 X 10 -24 kg m s -1 = 1.37 x 10 -10 m

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