Transcript Document
Debroglie Wavelength Heisenberg Uncertainty Principle Operators Please turn off all downloads. You can usually pause them by clicking on them and clicking pause. Facebook and youtube are officially banned during class time (this is not me micromanaging, it’s a legit internet issue as told to me by OIT). • Visit: https://checkin.ics.uci.edu/ • Log in and select Chem 1A. • When prompted, type the word of the day: IS WILL BE GIVEN IN CLASS. • Ensure when asked if you will share your location you select “allow”. • Visit: https://learningcatalytics.com/ • Sign in MasteringChemistry account name • When prompted, type session ID: THIS WILL BE GIVEN IN CLASS. DeBroglie Wavelength: Matter has a wavelength too • The average speed of a helium atom at 25 C is 1.23x103m/s. What is the average wavelength of a helium atom at this temperature? How does this compare to the size of the helium atom (140 pm)? Can this equation be used for light? How do you know? Heisenberg Uncertainty Principle: An analogy • Heavy object being hit by tennis balls • • Light object being hit by tennis balls • QUESTION 3 • Question 3- Which statement(s) are correct according to the Heisenberg Uncertainty Principle. (Note: Light does have momentum, although its not calculated by its mass (it has no mass) but rather by its wavevector, something we won’t go into in this class, you just need to know that it does have momentum to answer this question) • A) You cannot simultaneously know the velocity and position of matter • B) You cannot simultaneously know the momentum and position of matter • C) You cannot simultaneously know the momentum and position of light • D) It exists because our measurements are not accurate enough • E) It exists due to the duel nature in all things QUESTION 4• Use the Heisenberg uncertainty principle to calculate the uncertainty in meters in the position of a honeybee weighing 0.68g and traveling at a velocity of 0.85 m /s. Assume that the uncertainty in the velocity is 0.10m/s. • How does this compare to the size of the bee? Operators: Math Background Time The video and next class will deal with the chemistry and practical upshots of this. For now, lets just see how it works in a mathematical sense. • Definition of “operator”: a function acting on the space of physical states • over-simplify that to: a function that acts on a particular type of function instead of a number • Definition of eigenvalue: non-zero vector that when a matrix is multiplied by it yields a constant multiple • over-simplify that to: the number that is returned when a particular operator (Hamiltonian) acts on a particular function, such that the same function, times a number, is given back.