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Chapter 7 General

by: Cassandra Danhof

Chapter 7 General CHEM 1411

Cassandra Danhof
Lone Star College-CyFair
GPA 3.21

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These notes go over the wave nature of light, quantum effects and protons, the Bohr theory of the Hydrogen atom, quantum mechanics, and quantum numbers and atomic orbitals.
General Chemistry I
Prof. Chakranarayan
Class Notes
General Chemistry
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This 9 page Class Notes was uploaded by Cassandra Danhof on Saturday September 24, 2016. The Class Notes belongs to CHEM 1411 at Lone Star College-CyFair taught by Prof. Chakranarayan in Fall 2016. Since its upload, it has received 11 views. For similar materials see General Chemistry I in Chemistry at Lone Star College-CyFair.

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Date Created: 09/24/16
General Chemistry Chapter 7: Quantum Theory of the Atom Learning Objectives Important Terms 7.1 The Wave Nature of Light Define the wavelength and frequency of a wave Wave: A continuously  ● The wavelength is the distance between a high  repeating change or  point on a wave oscillation in matter or in  a physical field  Wavelength ( λ ): The  distance between any  two adjacent identical  points of a wave that's  fixed in one unit of time  ● The frequency is how many wavelengths there are  (usually a second). The  in a specific point in time  unit for wavelength is 1/s  −1 or  s , which is also  called Hertz (Hz). Frequency ( ν ): The  number of wavelengths of that wave that pass a  fixed point in one unit of  time  Electromagnetic  Spectrum: The range of  ● Inverse relationship between the frequency and  frequencies or  the wavelength ● Total length of the wave that passes a fixed point avelengths of  electromagnetic radiation in unit time =νγ  (speed of the wavelength) ○ Speed of the wave =  νγ ● c=νγ c c ○ v=  , γ= γ v Relate the wavelength, frequency, and speed of light (Examples  7.1 and 7.2) ● What is the wavelength of the yellow sodium  14 emission, which has a frequency of 5.09 10 /s ○ The frequency and wavelength are  related by the formulac=νγ . Yoo rearrange  c the formula to gi eγ= ν ○ In which c is the speed of light (3.00 8 x  10 m/s ). Substituting yields  3.00x10 m/s ○ γ= 14 = 5.89 x 5./09x10 /s 10−7 m or 589 nm ● What is the frequency of violet light with a  wavelength of 408 nm? ○ You rearrange the equation relating  c frequency and wavelength to giv  ν= λ ○ Substituting for  λ  (408 nm = 408 x  −9 m) gives  10 8 3.00x10 m/s ○ ν= −9 = 7.35 x 408x10 m 10 /s Describe the different regions of the electromagnetic spectrum ● Electromagnetic radiation is a form of energy from  the transfer of electrons   7.2 Quantum Effects and Photons State Planck’s quantization of vibrational energy Plank’s Constant: A  ● Planck’s proposed that all atoms in a solid vibrate physical constant relating with a definite frequency depending on the solid, althougenergy and frequency,  they could only hold certain quantized energies of  having the value vibration, defined atE=nhv −34 −34 6.63x10 J∙s ● Planck’s constant ( 6.63x10 J∙s ) is the  Photons: Particles of  constant of energy and frequency electromagnetic energy,  Define Plank’s constant and photon with energy E  ● E = nhv ← vibrational energy of atom proportional to the  ● V = frequency observed frequency of  ● H =  6.63 x10 −3J∙s light  Photoelectric Effect: The  ● n= a quantum number, always a whole number  (ex. 1,2,3) ejection of electrons from  ● Ephotonv ← Planck’s constant (photon) the surface of a metal or  Describe the photoelectric effect from another material  ● The photoelectric effect is when light hits the  when light shines on it  surface of one area, the electrons bounce off and the  Particle­Wave Duality of  photon gets absorbed Light: Light have  properties of both waves  and matter; neither  understanding is  sufficient alone  Calculate the energy of a photon from its frequency or wavelength (example 7.3) ● The red spectral line of lithium occurs at 671 nm  (6.71 x  10 m ). Calculate the energy of one photon of  this light  ○ The frequency of this light is  c 3.00x10 m/s ○ ν= = = 4.47 x λ 6.71x10 m7 14 10 /s 7.3 The Bohr Theory of the Hydrogen Atom State the postulates of Bohr’s theory of the hydrogen atom Continuous Spectrum: A  ● Energy Level Postulate: An atom can only have a  spectrum containing light  specific energy level of all wavelengths −R H Line Spectrum: A  ○ E= 2  n= 1,2,3…  spectrum showing only  n ○ R =2.179x10 −18J certain colors or specific  H wavelengths of light.  ● Transition Between Energy Levels: The only way  When atoms are heated,  an electron can change is if it goes through a transitionthe emit light. This  from one energy level to the next process produces a line  ○ An electron on higher energy goes  spectrum that is specific  through a transition to a lower energy level,  to that atom.  releasing a photon in the process  Energy Levels: Specific  Relate the energy of a photon to the associated energy levels ofenergy values of an atom an atom ● Energy of emitted photon = hv = ­E = ­ (Ef ­ Ei) 1 1 ● hv=R (H − ) n2f ni ● In Balmer’s formula, the quantum number  nf is  2 Determine the wavelength or frequency of a hydrogen atom  transition (example 7.4) ● What is the wavelength of light emitted when the  electron in a hydrogen atom undergoes a transition from  energy level n = 4 to n = 2  ● From the formula for the energy levels, you know  that  ○ ❑ −Rh −R H −R H −R H E i 2 = ∧E f 2 = 4 16 2 4 ○ You subtract the lower value from  the higher value, to get a positive result (the  energy of the photon is positive. If you result is  negative, it means you calculatedfE i ,  rather than  −E . Simply reverse the  i f subtraction to obtain a positive result). Because  this results equals the energy of the photon, you  equate it to hv: −R H 4 −4R +16R ○ ) =  H H −R H 64 ( 16 )−¿ −R +HR H 3R H =  16 =  16 =hv ○ The frequency of the light emitted is  ○ −18 3 RH 3 2.179 x10 J 14 v= 16 = 16 ∙ −34 =6.17 x10 /s h 6.626 x10 J ∙s ○ Since  γ=c/v ○ 3.00x10 m/s −7 γ= 14 =4.86x10 m∨486nm 6.17x10 /s ○ The color is blue­gr  n Describe the difference between emission and absorption of light  by an atom ● Emission is of light by an atom occurs when the  electron undergoes a transition of upper level energy to  lower level (ex. n=3 to n=2) ● Absorption of light occurs when the electron  undergoes a transition of lower level energy to higher level energy (ex: n=2 to n=3) 7.4 Quantum Mechanics  State the de Broglie relation De Broglie Relation: ● Particles (matter) might also have wave propertiesγ=h/mv as well as matter properties  Quantum (wave)  ● The wavelength of a particle of mass, m(kg), andMechanics: The branch  velocity, v(m/s) is given by the de Broglie relation:of physics that  ○ λ= h   h=6.62 x10 −3J∙s mathematically describes  mn the wave properties of  Calculate the wavelength of a moving particle (Example 7.5) submicroscopic particles  Uncertainty Principle: A  ● A. Calculate the wavelength (in meters) of the  wave associated with a 1.00 kg mass moving at 1.00  relation that state that the km/hr.  product of the uncertainty ● B. What is the wavelength (in picometers)  in position and the  uncertain relation that  associate−31ith an electron, whose mass is 9.11x10 kg , traveling at a speed of states that the product of  4.19x10 m/s ? (This speed can be attained by an  the uncertainty in position and the uncertainty in  electron accelerated between two charged plates diffemovement of a particle  by 50.0 volts; voltages in kilovolt range are used incan be no smaller than  electron microscopes ● A: Planck’s constant divided  by  4 π ○ A speed or  v of 1.00 km/hr  equals km 1hr 10 m ○ 1.00 x x hr 3600s 1km ¿2.38x10−33m ❑ ○ Substituting quantities (all  expressed in SI units for consistency), you get  h 6.63x10−34J∙s ○ λ= = mv 1.00kgx0.278m/s ¿2.38x10−33m ● B  ○ h 6.63x10−34J ∙s γ= = −31 6 mv 9.11x10 kgx4..19x10 m/s ¿1.74x10−10m=174nm Define quantum mechanics ● Quantum (wave) mechanics is a properties that  mathematically describes the wave properties of  subatomic particles  State Heisenberg's uncertainty principle  ● An uncertainty in position can be no smaller than  Planck’s constant divided b4 π ○ Δ x=uncertainty∈position ○ Δ p=uncertainty∈momentum h ■ (Δ x)(Δ p)≥ 4π ● The smaller the mass of the object, the more  uncertainty there is  Relate the wave function for an electron to the probability of  finding it at a location in space  ● Solving Schrodinger's equation gives a wave  function, psiψ , which gives information about a  particle in a given energy level  gives you the  ψ electron’s momentum in space  7.5 Quantum Numbers and Atomic Orbitals Define atomic orbital (wave function)  Atomic Orbital: A wave  ● The region of space where the electrons have  function for an electron in definite shape and are most likely by the atom. an atom Define each of the quantum numbers for an atomic orbital and  Principal Quantum  give its rules  Number (n): The one on  ● Principal Quantum Number (n): (positive values  which the energy of an  1,2,3,4…) The energy of an electron depends on n.  electron in an atom  ○ The smaller n is, the lower the  principally depends; it  energy.  can have any positive  ○ Also the orbital size depends on n.  value; 1,2,3 and so on The larger the atom, the larger the orbital.  Angular Momentum  ○ Orbitals of the same quantum state  Quantum Number (I):  n are said to belong to the same shell. Distinguishes orbitals of  given n having different  shapes; it can have any  Letter  K L M N... integer value from 0 to n­ n 1 2 3 4... 1 Magnetic Quantum  Number ( m ):  ● Angular Momentum Quantum Number ( l ):  l Distinguishes shape of the orbital Distinguishes orbitals of  given n and l ­ that is, of  ○ For each n, there are n kinds of  given energy and shape  orbitals with a distinguishable shape denoted by abut having a different  quantum number  ○ l: 0 to (n­1) number of values orientation in space; the  allowed values are the  l  will be the same as n integers from ­l to +l. ○ Ex:  Spin Quantum Number     ■ n=1  ● ( m s : Refers to the  two possible orientations  l=0(s) of the spin axis of an  ■ n=2 electron; possible values  ● l=0(s) +1 −1 ←-orbitals that correspond are  2 and  2 ● l=1(p) ■ n=3 ● l=0(s) ● l=1(p) ● l=2(d) ■ n=4 ● l=0(s) ● l=1(p) ● l=2(d) ● l=3( f ) ○ Orbitals that have the same n but  different l are said to belong to different subshells  go a given shell Lette s p d f g... r l 0 1 2 3 4... ● Magnetic Quantum Number ( ml ) m : ○ l number of values2l+1 );  values of  l−l ,¿0¿+l ○ Ex.  ■ n=4 ● l=0(s) ○ ● l=1(p) ○ ● l=2(d) ○ ● l=3( f ) ○ ● Spin Quantum Number ( m s : The two possible  +1 ∧−1 orientations of an electron's axis; known as  2 ○ This is important when looking at  orbital configurations Apply the rules of quantum numbers (example 7.6)  ● State whether each of the following sets of  quantum numbers is permissible ofr an electron in an  atom. If a set is not permissible, explain why. +1 ○ A. n= 1 ,  l=1,m =lm = s 2 ■ Not permissible. The l  quantum numebr is equal to n; it must  be less than n −1 ○ B.n=3,l=1,m =−l.m = s 2 ■ Not permissible. The  magnitude of the  m l quantum number  m (that is, the  l value, ignoring its sign)  must not be greater than l +1 ○ C .n=2,l=1.m =lm = s 2 ■ Permissible ○ D.n=2,l=0,m =0,m =1 l s ■ Not permissible. The +1 m s quantum number can only be  2 −1 and  2 Describe the shapes for s, p and d orbitals 


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