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# HW4 - Homework#4 Your Name Due on Friday October 28 before...

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Homework #4 Your Name: Due on Friday, October 28, before the lecture. Only two problems will be graded explicitly. [Remark: Comment I have heard: “Learning science is like eating dark chocolate—bitter at the beginning and sweet at the end”. We have gone far and deep in this course; let’s celebrate our accomplishments by seeing how these principles apply to real-life research. In this homework, you will see some applications of “particle in a box” to modern chemistry. If you still feel very bitter, please find resources and assistance ASAP. We are here for you.] 1) For a particle in a 1-D box, the possible values of the total energy are 2 2 2 8 ma n h E . Calculate the splitting between the energy levels 1 and 2 (i.e. corresponding to n =1 and n =2) for i. an electron in a box of the length a = 1 nm ii. yourself in a box of a size a = 1 nm (provided you can fit). What is the implication of this latter result? Can your quantum nature (quantization of energy spectrum) be observed in the box of this size? Are you classical or quantum, in these conditions?

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