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The proabability density of an electron

  1. Jul 31, 2008 #1
    1. The problem statement, all variables and given/known data
    The following is a graph of |(x)|^2


    Question is.

    What is the probability that an electron will be detected ina 0.0010-cm-wide region at x = 0.50 cm? At x= 0.999 cm?
    b) If 10^4 electrons are detected, how many are expected to land in the interval -0.30 cm - 0.30 cm.

    Also, lets suppose that this was a graph for the |(x)|^2 of a neutron.
    How you you find the value 'a' if it wasn't given?

    2. Relevant equations

    I know that Probability of landing at x = (probability density at x )* (length)
    Also know that expected value = number of electrons * probability.

    But I am having trouble putting these two together. Can some please show me how to do this question?

    3. The attempt at a solution

    So I think the probability density at 0.50 cm is 0.5 cm^-1 (reading the graph, the slope is -1 so the y value seems to be 0.5 cm^-1)

    So P(x) = 0.5 cm^-1* 0.0010 cm = 0.0005? But the answer is 0.005

    And I have no idea how to find 'a' by using only the information from the graph.

    Can someone help me with this whole concept?
  2. jcsd
  3. Jul 31, 2008 #2
    I meant graph of |psi (x)|^2
  4. Jul 31, 2008 #3
    I think your graph's horizontal axis should be labeled in cm.

    The slope of your probability density function on the positive-x side is positive one.

    To find a, you need to consider the integral of your (or any) probability function from negative infinity to positive infinity.
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