General Chemistry I
General Chemistry I CHM 2045
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Chapter 7 The Quantum Mechanical Model of the Atom Rutherford s Model Inside an Atom Electron Orbit Nucleus 2003 HowSKuMWurks The Behavior of the Very Small 0 Electrons are incredibly small 0 Electron behavior determines much of the behavior of atoms 0 Directly observing electrons in the atom is impossible the electron is so small that observing it changes its behavior Quantum Mechanical Model 0 Explains the manner electrons exist and behave in atoms 0 Helps us understand and predict the properties of atoms that are directly related to the behavior of the electrons V why some elements are metals while others are nonmetals V why some elements gain 1 electron when forming an anion while others gain 2 V why some elements are very reactive while others are practically inert V and other Periodic patterns we see in the properties of the elements The Wave Nature of Light 0 A wave is a continuously repeating change or oscillation in matter or in a physical field Light is also a wave gt It consists of oscillations in electric and magnetic fields that travel through space gt Visible light X rays and radio waves are all forms of electromagnetic radiation Electromagnetic Radiation Eieetrzi ci fif ldi M agne tic ld39i Direction of travel Copyright 2008 Pearson Prentice Hall Inc The Wave Nature of Light 0 A wave can be characterized by its wavelength and frequency 0 The wavelength 7 lambda is the distance between any two adjacent identical points of a wave 0 The frequency u nu of a wave is the number of wavelengths that pass a fixed point in one second Wavelenglh Amplitude V Direction of wave propagalion Wavelength b d Wavelength gt K V Amplitude V Ampl AAAAAWAA V VVVVVV The Wave Nature of Light 0 The product of the frequency v waves sec and the wavelength 9 m wave would give the speed ofthe wave in ms 0 In a vacuum the speed oflight c is 300 X 108 ms Therefore cvk 0 So given the frequency of light its wavelength can be calculated or vice versa Zxamyl39e Calculate the wavelength of red light with a frequency of 462 X 1014 s 1 Given Find Concept Plan Relationships Solve Check Practice Calculate the wavelength of a radio signal with a frequency of 1007 MHZ 10 Electromagnetic Spectrum 0 The range of frequencies or wavelengths of electromagnetic radiation is called the electromagnetic spectrum Visible light extends from the Violet end of the spectrum at about 400 nm to the red end with wavelengths about 800 nm Beyond these extremes electromagnetic radiation is not Visible to the human eye Electromagnetic Spectrum I 10quot m 10 0 107 I0y 10 In Wavelenglhmm I I 3 10 10 m to 10 10 mquot 104 mqucncy Hz I x x x x I x x 1 x rays 1m Infmcd Microwave Rndm waves rays viulet gt l39ype ufmdiauon n TV FM radio v HF TV AM radio Micmwm mcns pulls u call salell csmmns xelephunes 700 mu nm 500 mm Continuous Spectrum Copyright 2008 Pearson Prentice Hall Inc White light spectrum 13 The Photoelectric Effect 0 It was observed that many metals emit electrons when a light shines on their surface this is called the Photoelectric Effect 0 Classic wave theory attributed this effect to the light energy being transferred to the electron 0 According to this theory if the wavelength of light is made shorter or the light waves intensity made brighter more electrons should be ejected 14 The Photoelectric Effect The Photoelectric Effect Light quot VEvacuated 39 chamber Metal surface I l Current meter Light Voltage source Emitted electrons a 0 Copyright 2008 Pearson Prentice Hall Inc 15 The Photoelectric Effect The Problem 0 In experiments with the photoelectric effect it was observed that there was a maximum wavelength for electrons to be emitted called the threshold frequency regardless of the intensity 0 It was also observed that high frequency light with a dim source caused electron emission without any lag time 16 Nature of Light gt Einstein proposed that the light energy was delivered to the atoms in packets called quanta or photons gtIn 1905 Albert Einstein proposed that light had both wave and particle properties as observed in the photoelectric effect gt Einstein based this idea on the work of a German physicist Max Planck Quantum Effects and Photons 0 Planck s Quantization of Energy 1900 According to Max Planck the atoms of a solid oscillate with a definite frequency V I He proposed that an atom could have only certain energies of Vibration E those allowed by the formula E nhv where h Planck s constant is assigned a value of 663 X 10393415 and v must be an integer Quantum Effects and Photons 0 Planck s Quantization of Energy Thus the only energies a Vibrating atom can have are hv 2hv 3hv and so forth 7 The numbers symbolized by n are quantum numbers 7 The Vibrational energies of the atoms are said to be quantized Example 72 Calculate the number of photons in a laser pulse with wavelength 337 nm and total energy 383 m Given Find Concept Plan Relationships Solve 20 Prac ce What is the frequency of radiation required to supply 10 X 102 of energy from 85 X 1027 photons 21 Ejected Electrons 0 1 photon at the threshold frequency has just enough energy for an electron to escape the atom binding energy 1 0 For higher frequencies the electron absorbs more energy than is necessary to escape 0 This excess energy becomes kinetic energy of the ejected electron Kinetic Energy Ephoton Ebinding KE by 1 22 Spectra 0 When atoms or molecules absorb energy that energy is often released as light energy fireworks neon lights etc 0 When that light is passed through a prism a pattern is seen that is unique to that type of atom or molecule the pattern is called an emission spectrum noncontinuous can be used to identify the material gt ame tests 0 Rydberg analyzed the spectrum of hydrogen and found that it could be described with an equation that involved an inverse square of integers 1097gtlt107m391 i L n1 Hz 23 Emission Spectra Emission Spectra Prism separates component wavelengths Photographic Hydrogen Hydrogen l39Il spectrum lamp Exciting Gas Atoms to Emit Light with Electrical Energy 25 Examplee f Speetm Helium spectrum Barium spectrum Oxygen spectrum IIIIIIIIIIIIIIMWI Neon spectrum 26 Bohr s Model 0 Neils Bohr proposed that the electrons could only have very specific amounts of energy fixed amounts quantized 0 The electrons traveled in orbits that were a fixed distance from the nucleus stationary states 0 Electrons emitted radiation when they jumped from an orbit with higher energy down to an orbit with lower energy the distance between the orbits determined the energy of the photon of light produced 27 434 nm Violet eB r o Ind quotoSectra 486 nm Blue green 657 nm Red Copyright 2008 Pearson Prentice Hall Inc 28 Quantum Mechanics 0 Bohr s theory established the concept of atomic energy levels but did not thoroughly explain the wavelike behavior of the electron 0 Current ideas about atomic structure depend on the principles of quantum mechanics a theory that applies to subatomic particles such as electrons 29 Wave Behavior of Electrons de Broglie proposed that particles could a have wavelike character quot quot 1 Because it is so small the wave m character of electrons is significant 3 Electron beams shot at slits show an interference pattern the electron interferes with its own wave de Broglie predicted that the 5 fe WOW wavelength of a particle was inversely 18924987 proportional to its momentum k 2 h g Mm S mass kg 0 veloc ity m s39l 30 Quantum Mechanics 0 If matter has wave properties why are they not commonly observed I The de Broglie relation shows that a baseball 0145 kg moving at about 60 mph 27 ms has a wavelength of about 17 X 103934 m 13 539quot quot7 o This value is so incredibly small that such waves cannot be detected Example Calculate the wavelength of an electron traveling at 265 X 106 ms Given Find Concept Plan Relationships Solve 32 Hactz39ce Determine the wavelength of a neutron traveling at 100 X 102 ms Mass 1675 X 1024 g neutron 33 Complimentary Properties 0 When you try to observe the wave nature of the electron you cannot observe its particle nature and Visa versa wave nature interference pattern particle nature position which slit it is passing through 0 The wave and particle nature of nature of the electron are complimentary properties Vas you know more about one you know less about the other 34 Uncertainty Principle 0 Heisenberg stated that the product of the uncertainties in both the position and speed of a particle was inversely proportional to its mass V X position AX uncertainty in position V V velocity Av uncertainty in velocity W uMky 79077976 Vrn mass 0 This means that the more accurately you know the position of a small particle like an electron the less you know about its speed AxxAin i 47 m 35 V and visaversa Determinacy vs Indeterminacy According to classical physics particles move in a path determined by the particle s velocity position and forces acting on it determinacy definite predictable future Because we cannot know both the position and velocity of an electron we cannot predict the path it will follow indeterminacy indefinite future can only predict probability The best we can do is to describe the probability an electron will be found in a particular region using statistical functions 36 Quantum Mechanics 0 Although we cannot precisely define an electron s orbit we can obtain the probability of finding an electron at a given point around the nucleus gt Erwin Schrodinger defined this probability in a mathematical expression called a wave function denoted w psi Erwin Schrodinger gt The probability of finding a particle in a region of 18871961 space is defined by W gt The probability map for an electron is called an orbital Wave Function q 0 Calculations show that the size shape and orientation in space of an orbital are determined be three integer terms in the wave function 0 These integers are called quantum numbers principal quantum number n angular momentum quantum number I magnetic quantum number m 38 Principal Quantum Number 0 The principal quantum numbern represents the shell number in which an electron resides The smaller n is the smaller the orbital The smaller n is the lower the energy of the electron 1 n 2 I IIIII I I39 n 3 IllIIIIIIIIIIII lullIIIIIIIII n4 IIIIIIIIIIIII Principal Energy Levels in Hydrogen A Energy E4 136 gtlt1019J n 4 3 E3 242 X10 19 n 2 E2 545 gtlt10 19 n 1 E1 218 X10 18 Copyright 2008 Pearson Prentice Hall Inc 40 Electron Transitions 0 In order to transition to a higher energy state the electron must gain the correct amount of energy corresponding to the difference in energy between the final and initial states 0 Electrons in high energy states are unstable and tend to lose energy and transition to lower energy states 0 Each line in the emission spectrum corresponds to the difference in energy between two energy states Excitation and Radiation Light is emitted as electron falls back to lower energy level Energy 3 ll N Electron absorbs energy and is excited to unstable energy level 41 Copyright 9 2008 Pearson Prentice Hall Inc Hydrogen Energy Transitions Level nm n5 n4 486nm 1 n3 Infrared 434 nm 656 nm wavelengths n2 Visible wavelengths Ionization n1 Ultraviolet wavelengths 42 Angular Momentum Quantum Number 0 The angular momentum quantum number I distinguishes sub shells within a given shell that have different shapes Each main shell is subdivided into sub shells Within each shell of quantum number n there are n sub shells each with a distinctive shape I can have any integer value from O to n 1 The different subshells are denoted by letters Letter 5 p d f g I O 1 2 3 4 43 Probability amp Radial Distribution Functions 0 w2 is the probability density the probability of finding an electron at a particular point in space for s orbital maximum at the nucleus decreases as you move away from the nucleus 0 The Radial Distribution function represents the total probability at a certain distance from the nucleus maximum at most probable radius 0 Nodes in the functions are where the probability drops t0 0 Nodes 1quot 5 7 r V Copyright 2008 P eeee on Prenti cccc II Inc 44 Probability Density Function g gt 3 Height of curve Density of dots 03 proportional to proportional to 33 probability densrty 1112 probability density lbz 8 O n r b Copyright 2008 Pearson Prentice Hall Inc 45 Radial Distribution Function 15 Radial Distribution Function Maximum at 529 pm Total radial probability I I I I 0 200 400 600 800 1000 Distance from the nucleus r pm Copyright 2008 Pearson Prentice Hall Inca I O the sorbital a Each principal energy is orbital surface state has 1 S orbital Z 0 Lowest energy orbital in a principal energy state 0 Spherical 0 Number of nodes n 1 Copyright 2008 Pearson Prentice Hall Inc 47 Total radial probability Probability density W2 rHOOPm 6 amp z r100pm i i z 4 rumipml 5 l l I 8 8 Zsand 3S Total radial probability Probability density W2 r100 pm 48 Magnetic Quantum Number 0 The magnetic quantum number m distinguishes orbitals within a given subshell that have different shapes and orientations in space Each sub shell is subdivided into ORBITALS each capable of holding a pair of electrons m can have any integer value from I to 1 Each orbital within a given sub shell has the same energy 49