Download Electron Experiments: Probability Distributions & Quantum Mechanics in Slit - Prof. David and more Assignments Physics in PDF only on Docsity! Phys 100 Spring 2009 Concepts of Physics: Homework 11 Due: 29 April 2009 1 Hobson, Physics: Concepts and Connections, Ch. 13 Conceptual Exercise 10, page 318. 2 Hobson, Physics: Concepts and Connections, Ch. 13 Review Question 14, page 318. 3 Hobson, Physics: Concepts and Connections, Ch. 13 Conceptual Exercise 18, page 318. 4 Particles Passing Through a Single Slit A beam of electrons is fired toward a barrier which is impenetrable everywhere except through slit, which is so narrow that an electron can only just pass through. The initial direction of each electron’s motion is vertical (absolutely no horizontal component). The probability distribution (curve) for the electron’s arrival at various points along the screen is illustrated in Fig. 1. Slit Electrons Screen Probability of electron arrival. ∆x A B Figure 1: Single slit electron experiment. a) Suppose that an electron arrives at the screen. In this case what would be a reasonable answer to the question: “Did the electron passed through the slit or not?” b) Is it possible for an electron to hit the screen at point A? 1 c) Is it possible for an electron to hit the screen at point B? d) Only those electrons that were aimed precisely at the slit will ever pass through and their states of motion prior to arrival at the slit will be identical. What does this probability distribution imply regarding the point at which any one of these electrons strikes the screen? Will it always strike the screen at the same point? e) In this scenario, all that the electrons all started with the same initial state of motion. Compare this to dropping a set of balls from the same point through a sufficiently wide slit. Would they all land at the same spot? Would your intuition (or equivalently classical physics) predict that the electrons will arrive at the same point on the screen? How does this compare to your answer to part (d)? f) Is the physical world deterministic (i.e. the future state of a physical system only depends on its current state and the interactions it experiences) or is it contain elements of randomness? Justify your answer based on answers to previous parts of this question. 5 Particles passing through a double slit Consider a beam of electrons fired at a double slit barrier as illustrated in Fig. 2. Each electron which passes through the left slit is painted red by an ink jet without affecting its motion. Those passing through the right are painted blue. Fig. 2 shows the probability distributions for finding red and blue electrons at locations on the screen. Slit Electrons Screen Figure 2: Two single slits with color markers. a) The electron color describes through which slit it passed. Determine the probability with which an electron arrives at various points on the screen, regardless of the color. Sketch the probability distribution for this. b) Now suppose that the ink jets are turned off. Again, one aims to determine the proba- bility distribution for an electron hitting the screen. A remarkable feature of quantum physics that the intuitive answer to this is completely incorrect. The probability distri- bution is illustrated in Fig. 3. 2
