Lecture 8 - Quantum Theory I

Tuesday, February 6, 2024

7:18 AM

 

 

 Class notes can now be found in an alternative location: https://bricejurban.github.io/CHEM111/ I will update this on Tues/Thurs evenings This is HTML based and compatible with all devices (no more issues!) Only downside is that hyperlinks do not work. Assignments due this week: ﷟HYPERLINK "https://boisestatecanvas.instructure.com/courses/28699/assignments/990937"HW 4 - Quantum Part 1 (Aktiv Chemistry) (Sun 2/11) Finish reading Chapter 4 Read Chapter 5 Assignments due next week: ﷟HYPERLINK "https://boisestatecanvas.instructure.com/courses/28699/assignments/990975"HW 5 - Quantum Part 2 (Aktiv Chemistry) (Fri 2/16) Reading quiz TBD New Activity TBD Read Chapter 6, Preview 7 Office Hours: Friday 11-1 CIC ﷟HYPERLINK "https://calendly.com/bricejurban/office-hours"By appointment Midterm 1: The first midterm is graded and available for review using the Gradescope software which can be found on Canvas. Click through each question's rubric to see how you were graded. I recommend printing a copy then reviewing the answer key in the big display case outside SCNC 336 next to the chemistry computer lab. See map for location of answer key. After reviewing, if you notice any discrepancies you can submit a regrade request through Gradescope. Statistics: Mean 73% Median 77% Standard deviation 20% Top score 106% Your lowest midterm grade for the semester will be dropped from the gradebook. Midterms amount for 40% of your course grade. If you did not do as well as you would have hoped, you may need to adjust how you study for this class. Here are some ﷟HYPERLINK "https://boisestatecanvas.instructure.com/courses/28698/modules/items/2913696"suggestions. Today's Schedule: Tuesday (2/6) Photoelectric Effect Wave-Particle Duality of Light and Matter de Broglie wavelength Bohr Model Heisenberg Uncertainty Principle Looking Ahead Thursday (2/8) Schedule Quantum Numbers and Orbitals Electron Configuration Ground state Excited State Transition metals Atomic Radii AnswerKey.png SCALE: REV: / 04 Ill 2 3 CAMPUS LN 1 0 20 0 工 ○ C 二 丄 冖 凵 工 一 工 」 , qen Jalndtuoo s 一 go 山 00 」 00 ; ; S ! 山 0 0 0 O•h•ue 」 。 」 。 。 56 冖 冖 凵 POOuedPV Equations and Constants to know how to use from last class
Equations and Constants to know how to use from last class 𝜆𝜈=𝑐 wavelength(𝜆)-frequency (𝜈) relation c = 2.998 × ﷐10﷮8﷯ m∙﷐s﷮−1﷯ speed of light 𝐸=ℎ𝜈 𝑜𝑟 E=﷐hc﷮λ﷯ Planck-Einstein Equation i.e. Energy of a photon h = 6.626 × ﷐10﷮−34﷯ J ∙𝑠 Planck constant Equations to know how to use from today's class ﷐𝐸﷮𝑘﷯=ℎ𝜈−ℎ﷐𝑣﷮0﷯ (when 𝜈> ﷐𝜈﷮0﷯) ﷐𝐸﷮𝑘﷯=ℎ𝜈−𝜑 photoelectric equation (or in terms of the work function 𝜑) ﷐E﷮k﷯ = ﷐1﷮2﷯m﷐𝓋﷮2﷯ Kinetic energy equation 𝓋 = velocity not frequency 𝜆= ﷐ℎ﷮𝑚𝓋﷯ de Broglie wavelength used to find wavelength of electron, particle or anything with mass ﷐𝐸﷮𝑛﷯=﷐−2.1799 𝑎𝐽﷮﷐𝑛﷮2﷯﷯ (𝑛=1, 2, 3…) Energy levels (n) of hydrogen ﷐𝐸﷮𝑛﷯=−2.1799 𝑎𝐽﷐﷐𝑍﷮2﷯﷮﷐𝑛﷮2﷯﷯ (𝑛=1, 2, 3…) Energy levels (n) of one-electron ions (Z = atomic number) ﷐𝐸﷮𝑛﷯=2.1799 𝑎𝐽(﷐1﷮﷐﷐𝑛﷮𝑓﷯﷮2﷯﷯−﷐1﷮﷐﷐𝑛﷮𝑖﷯﷮2﷯﷯) Energy of an emitted photon transitioning from ﷐𝑛﷮𝑖﷯ 𝑡𝑜 ﷐𝑛﷮𝑓﷯ ﷐1﷮𝜆﷯=1.097 ×﷐10﷮7﷯ ﷐𝑚﷮−1﷯(﷐1﷮﷐﷐𝑛﷮𝑓﷯﷮2﷯﷯−﷐1﷮﷐﷐𝑛﷮𝑖﷯﷮2﷯﷯) ﷐Wavelength﷮−1﷯ of an emitted photon transitioning from ﷐𝑛﷮𝑖﷯ 𝑡𝑜 ﷐𝑛﷮𝑓﷯ ﷐𝐸﷮𝑛﷯=2.1799 𝑎𝐽(﷐1﷮﷐﷐𝑛﷮𝑖﷯﷮2﷯﷯−﷐1﷮﷐﷐𝑛﷮𝑓﷯﷮2﷯﷯) Energy of an absorbed photon transitioning from ﷐𝑛﷮𝑖﷯ 𝑡𝑜 ﷐𝑛﷮𝑓﷯ (Δ𝑥)(Δ𝑝)≥﷐ℎ﷮4𝜋﷯ 𝑝=𝑚∙𝓋 (Δ𝐸)(Δ𝑡)≥﷐ℎ﷮4𝜋﷯ Heisenberg uncertainty principle 𝛥𝑥=uncertainty in position Δ𝑝=uncertainty in momentum Momentum equation Energy-time uncertainty principle 1 atomic mass unit mass of an electron (me) mass of a proton (mp) mass of a neutron (mn)
1 atomic mass unit 1.6605 × ﷐10﷮−27﷯ kg mass of an electron (me) 9.1094 × ﷐10﷮−31﷯ kg mass of a proton (mp) 1.6726 × ﷐10﷮−27﷯ kg mass of a neutron (mn) 1.6749 × ﷐10﷮−27﷯ kg Helpful YouTube Videos from Professor Dave Explains that reviews today's material ﷟HYPERLINK "https://www.youtube.com/watch?v=7BXvc9W97iU&list=PLybg94GvOJ9FAFBqQGf5-4YbfKpWbJtGn&index=2"Quantization of Energy Part 1: Blackbody Radiation and the Ultraviolet Catastrophe ﷟HYPERLINK "https://www.youtube.com/watch?v=eU6VqGIc-2Q&list=PLybg94GvOJ9FAFBqQGf5-4YbfKpWbJtGn&index=3"Quantization of Energy Part 2: Photons, Electrons, and Wave-Particle Duality ﷟HYPERLINK "https://www.youtube.com/watch?v=au2HCVn9IJI&list=PLybg94GvOJ9EbbO2RXPWTUNIIE0C7hSfm&index=13"Bohr Model of the Hydrogen Atom ﷟HYPERLINK "https://www.youtube.com/watch?v=O6g-7rUgrdg&list=PLybg94GvOJ9FAFBqQGf5-4YbfKpWbJtGn&index=5"Quantum Mechanics and the Schrödinger Equation ﷟HYPERLINK "https://www.youtube.com/watch?v=7jY5Q6u65uo&list=PLybg94GvOJ9FAFBqQGf5-4YbfKpWbJtGn&index=6"The Heisenberg Uncertainty Principle Part 1: Position/Momentum and Schrödinger's Cat ﷟HYPERLINK "https://www.youtube.com/watch?v=_DXHrp6-LZI&list=PLybg94GvOJ9FAFBqQGf5-4YbfKpWbJtGn&index=7"The Heisenberg Uncertainty Principle Part 2: Energy/Time and Quantum Fluctuation Photoelectric Effect Max Planck solved the Ultraviolet Catastrophe by positing that blackbody radiation is emitted in small discrete packets called quanta An experiment that helped to provide evidence for this novel idea was the photoelectric effect experiment and Albert Einstein's interpretation of the results. Imagine a sheet of metal with a detector nearby that can monitor the ejection of electrons. Incident to the metal is a light source that can be changed in intensity or in frequency ﷟HYPERLINK "https://phet.colorado.edu/sims/cheerpj/photoelectric/latest/photoelectric.html?simulation=photoelectric"PhET Simulation (colorado.edu) - Try this experiment yourself! Untitled picture.png Intenslty 701 nt-n 0.000 current: o.oov I Untitled picture.png Intenslty 1 00*é 701 nt-n 0.000 current: o.oov I
Untitled picture.png Intenslty 701 nt-n 0.000 current: o.oov I Untitled picture.png Intenslty 1 00*é 701 nt-n 0.000 current: o.oov I Changing the intensity of red light has no effect on the number of electrons ejected Untitled picture.png Intenslty 450 nm o .020 current: 1.00 v I Untitled picture.png Intenslty 100% 450 nrn 0.051 current: 1.00 v I Going to a lower wavelength (higher frequency) of blue allows for the ejection of some electrons Increasing intensity of blue light produces a greater current Untitled picture.png Intenslt,' current: 0.340 Untitled picture.png 262 nn- current: Intenslty o .855
Untitled picture.png Intenslt,' current: 0.340 Untitled picture.png 262 nn- current: Intenslty o .855 Light in the UV results in much more electrons ejected Additionally the speed (kinetic energy) of the electrons is much greater If we plot the electron kinetic energy against light frequency we will observe a linear equation that has a x-intercept that does not pass through zero. This x-intercept is the minimum threshold frequency ﷐𝑣﷮0﷯ The work function (𝝋) is the energy ℎ﷐𝑣﷮0﷯ Only if light was quantized would this be possible! This can be mathematically represented by this equation: ﷐𝐸﷮𝑘﷯=ℎ𝜈−ℎ﷐𝑣﷮0﷯ ﷐when 𝜈> ﷐𝜈﷮0﷯﷯ or ﷐𝐸﷮𝑘﷯=ℎ𝜈−𝜑 The threshold frequncy of sodium metal is 5.51×﷐10﷮14﷯ Hz, when multiplied by h, it gives 0.341 aJ which is similar to the first ionization energy (0.85 aJ) We can then use the kinetic energy equation to find the velocity of the ejected electron: ﷐E﷮k﷯ = ﷐1﷮2﷯m﷐𝓋﷮2﷯ Untitled picture.png @ Electron energyvs light frequency 0.00 0.75 1.50 2.25 Frequency (xl onl 5 Hz) 3.00 Concept Check Given that the threshold frequency of caesium metal is 4.38 × 1014 Hz, calculate the velocity of an electron ejected from the surface of caesium metal when it is irradiated with light of wavelength 400.0 nm. The mass of an electron is 9.109 × 10–31 kg Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Light behaves as both a wave and a particle! But so do other particles In 1924, Louis de Broglie at age 32, proposed that matter under certain conditions could also exhibit wave-particle duality de Broglie put forth his idea as a simple equation: 𝜆= ﷐ℎ﷮𝑚𝓋﷯ where h is the Planck constant, m is mass in kg, and 𝓋 is the velocity in m/s An electron is one of the smallest subatomic particles and travels at speeds around the nucleus that approach the speed of light. It turns out that treating an electron just as a particle is incorrect. Evidence for this was first observed by J.J. Thomson's son G. P. Thomson by observing electron diffraction patterns ﷟HYPERLINK "https://www.youtube.com/watch?v=LC6WpitQeSo"Electron Diffraction De Broglie Waves and Nucleus Diameter Electron Diffraction De Broglie Waves and Nucleus Diameter - AQA A Level Physics Press enter to activate Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings 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Concept Check Calculate the de Broglie wavelength of a hydrogen molecule (H2) traveling at a speed of 2.0 × 103 m·s–1 The wavelength of the molecule is about the radius of an atom The energy levels in an atom are the result of the wave properties of the electron de Broglie's interpretation of the wave properties of matter, gave a plausible explanation for Niels Bohr's circular orbit theory of the atom Only when the wavelength of an electron matched complete revolutions was an orbit stable. The allowed energy states of the hydrogen atom are given by the equation: ﷐𝐸﷮𝑛﷯=﷐−2.1799 𝑎𝐽﷮﷐𝑛﷮2﷯﷯ ﷐𝑛=1, 2, 3…﷯ The integers n =1, 2, 3 . . . are allowed stationary states n = 1 is the ground state (lowest energy and most stable state) n = 2 is the first excited state n = 3 is the second excited state n = ∞ is when the atom is ionized and the electron is no longer bound Untitled picture.png 0 -2.00 n=6 n=5 n=3 Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Untitled picture.png 0 -2.00 n=6 n=5 n=3 Absorption of electromagnetic radiation of only specific energy differences will result in the promotion of an electron to a higher energy level Atoms can emit or absorb electromagnetic radiation to transition from one stationary state to another In lab this week you will be using a spectroscope to measure the emission spectra of various elements. You will also be observing the characteristic flame color of a variety of elements These spectral lines are the result of the difference in energy levels. For the data analysis you should be familiar with these three equations ﷐𝐸﷮𝑛﷯=2.1799 𝑎𝐽(﷐1﷮﷐﷐𝑛﷮𝑓﷯﷮2﷯﷯−﷐1﷮﷐﷐𝑛﷮𝑖﷯﷮2﷯﷯) Energy of photon emitted ﷐1﷮𝜆﷯=1.097 ×﷐10﷮7﷯ ﷐𝑚﷮−1﷯(﷐1﷮﷐﷐𝑛﷮𝑓﷯﷮2﷯﷯−﷐1﷮﷐﷐𝑛﷮𝑖﷯﷮2﷯﷯) E=﷐hc﷮λ﷯ The visible lines are known as the Balmer series are the transitions to the n = 2 energy level Untitled picture.png Brackett series Paschen series Balmer series Lyman series Concept Check A line in the Brackett series (En ⟶ E4) of hydrogen has a wavelength of 2626 nm. From what state (ni) did the electron originate? Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
A line in the Brackett series (En ⟶ E4) of hydrogen has a wavelength of 2626 nm. From what state (ni) did the electron originate? In what region of the spectrum is this line observed? Difference between Emission and Absorption Spectra Untitled picture.png 400 nm Sodium emission spectrum Sodium absorption spectrum 750 nm Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Untitled picture X-Rays Ix 10 12 1 x 10 14 Wavelength (in meters) 4 x 107 High Energy Gamma Rays 1 x 10 Ultraviolet Rays Ix108 5 x 107 Infrared Rays Visible Light 6 x 107 Radar -4 FM I x 102 TV Shortwave AM I x 102 7 x 107 Low Energy I x 104 Wavelength (in meters) Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Untitled picture.png 400 nm Sodium emission spectrum Sodium absorption spectrum 750 nm The Bohr Model is inconsistent with the Uncertainty Principle Werner Heisenberg showed that is not possible to accurately measure both the position (x) and momentum (p) of a particle simulatenously. When we try to observe a particle, we must use a photon. By very act of this observation, we manipulate the particle and this therefore results in some uncertainty in its momentum This is not a problem with our technique, but rather a fundamental limitation on accuracy. Heisenberg's discovery led to the quantum revolution a period during the 1920s to 1930s when our understanding of the atom changed dramatically. We will study this starting on Thursday. Here is Heisenberg's equation and a related one (note the inequality) (Δ𝑥)(Δ𝑝)≥﷐ℎ﷮4𝜋﷯ 𝑝=𝑚∙𝓋 (Δ𝐸)(Δ𝑡)≥﷐ℎ﷮4𝜋﷯ Heisenberg uncertainty principle 𝛥𝑥=uncertainty in position Δ𝑝=uncertainty in momentum Momentum equation Energy-time uncertainty principle Concept Check What is the uncertainty in the velocity of an electron whose position is known to within 2 × 10–8 meters? Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
If the electron is moving at a speed of 5.0 ×105 m·s–1, what fraction of this speed does the uncertainty represent? Consider a spectroscopic transition in a molecule that occurs within a very short time frame 1.0 × 10-15 seconds. This transition is due to an electron moving between two energy states in the molecule. (a) Calculate the minimum uncertainty in the energy (ΔE) of this transition. 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(b) Discuss might this uncertainty affect the results of spectroscopic measurements This will result in a broadening of the spectral line. Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings

 

 

 

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