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Charge densities within an atom

  1. Jan 18, 2010 #1
    1. The problem statement, all variables and given/known data
    A hydrogen atom might be modelled as a sphere of charge +e and radius 10-15 (the nucleus), surrounded by a sphere of charge −e and radius 10-12m (the electron cloud).
    (a) What is the average charge density of the nucleus? (b) What is the average charge density of the electron cloud?
    (c) What is the average charge density of the atom?
    (d) How much charge is contained within a radius of 5.0 × 10-13m? Give your answer in units of e.


    2. Relevant equations

    Volume of a sphere= (4/3)pi*r3


    3. The attempt at a solution

    I'm most looking for confirmation or corrections

    a) simply p= +e/((4pi/3)(10-15m)3)= approx +2.4 x 1044 e/m3

    b) p= -e/((4pi/3)(1 x 10-12m)3)= approx -2.4 x 1035 e/m3 ( I got the 1 x10-12m by subtracting total volume-nuclues volume)

    c) Would it just be zero because that's the only way we're going to get the zero net charge in the equation p=e/v

    d) The new radius emcompasses the nuclues so it's already +1e.
    then I did (4pi/3)(5.0x10-13m-10-15m)3= 5.2 x 10-37 m 3 then I multiply that volume by the electron density calculated at part B and got -.12 e. Finally 1-.12= +.88e as the final answer
     
  2. jcsd
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