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Distribution of charge in hydrogen atom

  1. Oct 20, 2015 #1
    Suppose the hydrogen atom consists of a positive point charge (+e), located in the center of the atom, which is surrounded by a negative charge (-e), distributed in the space around it.

    The space distribution of the negative charge changes according to the law p=Ce^(−2r/R), where C is a constant, r is the distance from the center of the atom, and R is Bohr's radius.

    Find the value of the constant C by using the electrical neutrality of the atom.

    I don't think I understand the charge distribution very well. I tried integrating the total negative charge of the sphere ( atom ), since I know it's equal to ( -e ).
     
    Last edited: Oct 20, 2015
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  3. Oct 20, 2015 #2

    Orodruin

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    Please show us what you did when you integrated the distribution.

    Edit: the model is really, really bad by the way, but for the sake of the problem, let us assume it is not.
     
  4. Oct 20, 2015 #3
    Без име.png
    Sorry about the format. I don't know if the last line makes sense.
    In the way I understand it the negative charge in a point should be p = Ce^(-2r/R). However I think i am wrong. Thank you in advance.
     
  5. Oct 20, 2015 #4

    Orodruin

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    You cannot do it like an integral in one dimension, the distribution is three dimensional.

    I see now that you really meant e^(-2r/R) with e being the base of the natural logarithm and not multiplication by the charge e. This is normally denoted by ^ or if you do not find that symbol by writing out "exp" for "exponential function".
     
  6. Oct 20, 2015 #5
    Yes, it's three dimensional, for a three dimensional point. But can't I integrate it for the whole radius, and then use the standard volume formula?
    Furthermore, I know Bohr's radius is the mean of the orbit, but can it be used to derive the radius of the atom.
     
  7. Oct 22, 2015 #6

    blue_leaf77

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    The modulus square of a wavefunction, ##p(r)## in your notation, describes the probability density of the electron and it has a dimension of inverse volume. You can therefore build the charge density ##\rho(r)## by multiplying ##p(r)## with the electron charge ##e##, so ##\rho(r) = e p(r)##. The total charge is then just the integral of this quantity over all space, not just until certain radius like you did there.
     
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