PH300 Spring Homework 07

Transcription

1 PH300 Spring 2011 Homework 07 Total Points: (1 Point) Each week you should review both your answers and the solutions for the previous week's homework to make sure that you understand all the questions and how to answer them correctly. You will receive credit for reviewing your old homework, which will be returned to you every Tuesday. Please review your homework and the solutions from last week and let me know that it was graded correctly. If it was not, state here which problems were incorrectly graded, and then contact me (via or before/after class). 2. (2 Points) Your first homework question this week is to submit one homework correction from the previous week's homework. Select one problem for which you had the wrong answer, and then: 1. Identify the question number you are correcting. 2. State (copy) your original wrong answer 3. Explain where your original reasoning was incorrect, the correct reasoning for the problem, and how it leads to the right answer. If you got all the answers correct, Great!!! Then state which was your favorite or most useful homework problem and why. 3. (1 Point) We can think more about the potential energy of an electron in the hydrogen atom by considering a negatively charged electron in the vicinity of a positively charged proton. If we define the potential energy of the electron as 0 when it is infinitely far from the proton, what is its potential energy when D = nm (in ev)? (Make sure to consider the sign of your answer.)

2 4. (1 Point) If we halve the distance, what happens to the potential energy of the electron? (Choose all that apply.) A) It becomes more negative. B) It becomes less negative. C) It becomes more positive. D) It becomes more positive. E) by a factor of 1/4. F) by a factor of 1/2. G) by a factor of 2. H) by a factor of 4. I) PE does not change. 5. (5 Points) The Bohr model postulates that electrons occupy circular orbits around the proton at the nucleus of the hydrogen atom; and do not radiate continuously (as required in classical electromagnetic theory). Bohr further postulated that the electron gained or lost energy by absorbing or emitting a photon of frequency (f), and, in doing so, jumped from one stationary state (orbit of radius r 1 ) to another stationary state (orbit of radius r 2 ). Since, in each stationary state, the electron-proton system has a specific total energy E(r), Bohr was assuming that: hf = E(r 2 ) E(r 1 ) Explain in your own words what this expression means. Consider the following questions in your response: What motivates its introduction (i.e., what is the connection to Einstein s conclusions based on the photoelectric effect)? Would the energy emitted or absorbed in the jumps have any direct relation to the orbital frequency of the electrons motion? Why have the absolute value (magnitude) signs? Under what conditions would the right hand side of the equation be positive and under what conditions would it be negative?

3 Problems Apply Bohr's model to the Hydrogen atom. (Be careful with signs here. Signs are important and the wrong sign means the wrong answer.) 6. (1 Point) Calculate the orbital radius (in nm) of the electron in the ground state. 7. (1 Point) Calculate the PE of the electron in this ground state (in ev). 8) (1 Point) Calculate the KE of the electron in the ground state (in ev). 9. (1 Point) What is the total energy of the electron in this ground state (in ev)? 10. (1 Point) You want to excite an electron in the ground state to the n = 3 level. What is the minimum kinetic energy (in ev) that a free electron colliding with an atom needs to have to do this? 11. (1 Point) What is the orbital radius in nm of the electron when it's at this higher level? 12. (1 Point) If an electron drops down from the n = 6 level to the n = 2 level, and then to the ground state of hydrogen, what colors of light will be emitted? (a) (0.5 pts) Photon color for n = 6 to n = 2 jump (in nm)? (b) (0.5 pts) Photon color for n = 2 to ground state jump (in nm)?

4 13. (1 Point) Bohr's model predicts spectra for any atom if it is ionized such that there is only one electron orbiting. Consider a doubly-ionized Li atom (3 protons, 1 electron). If the gray curve (same in each graph) represents the PE curve for hydrogen as a function of distance from the nucleus, which of the red curves represents the PE curve for Li++? 14. (0.5 Points) When the electron in Li++ is in its ground state, the radius of its orbit is that of the electron of the H atom in its ground state. A) 1/9 times B) 1/3 times C) 1/2 times D) the SAME as E) 2 times F) 3 times G) 9 times

5 15. (0.5 Points) and so the Li++ atom is the H atom: (Choose all that apply) A) smaller than B) the same size as C) larger than D) lighter than E) same mass as F) heavier than 16. (2 Points) The (classical) magnetic moment of a current loop is given by: m = I πr 2 where I is the current and r is the radius of the loop. Calculate the magnetic moment for an electron in the ground state of hydrogen (orbiting about a proton at the Bohr radius). This quantity is known as the Bohr magneton. Essay Questions refer to the reading 100 Years of Quantum Mysteries. 17. (3 Points) As discussed in this article, what were some of the problems in classical physics that led to the development of quantum theory? 18. (3 Points) How are the terms theory and interpretation used in this article? 19. (3 Points) Is there any experimental evidence in favor of any of the interpretations discussed in this article? In the cases where there is not, why would a scientist favor one interpretation over another?