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Density of chromium ions in ruby

  1. Mar 10, 2016 #1
    1. The problem statement, all variables and given/known data
    estimate the density of chromium ions in ruby, assuming that the concentration of chromium in ruby is about 0.05% by weight.

    2. Relevant equations
    decay rate = 0.5x10^3 s^-1
    answer: density N (sub T)= 1.6x10^19 cm^-3

    3. The attempt at a solution
    density = mass/volume
    density of ruby = 4.02 g/cm^3
    density of chromium = (4.02)(0.05) = .201 g/cm^3
    I know that this is wrong!
    What do I do?
     
  2. jcsd
  3. Mar 10, 2016 #2

    haruspex

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    It says "0.05%". Did you mean that or 5%?
     
  4. Mar 12, 2016 #3
    Yes, I really meant 0.05%.
     
  5. Mar 12, 2016 #4

    haruspex

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    But your calculation treated it as 5%.
    I believe you will also need the atomic mass of chromium.
     
  6. Mar 13, 2016 #5
    0.5*10^-3 = .0005 which = .05%

    lcr2139 treated it properly in the calculation (not to say that I have any idea what the calculation is, only that I know that 0.5*10^-3 = .05%)
     
  7. Mar 13, 2016 #6

    haruspex

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    The 0.5*10-3 was quoted as a decay rate, with the right units for that, which has nothing to do with the problem. (In fact, lcr wrote 103, not 10-3., but minus seems more likely for a decay rate.)
    In the calculation, lcr used 5% here:
     
    Last edited: Mar 13, 2016
  8. Mar 13, 2016 #7
    density of ruby: 4.02 g/cm^3
    molecular weight of chromium: 52 g/mol

    (4.02g/cm^3)*(.0005)*(6.022*10^23 atoms/mol) / (52 g/mol) = 2.32*10^19 cm^-3

    This is wrong! The real answer is NsubT= 1.6 * 10^19 cm^-3

    where am I going wrong?
     
  9. Mar 13, 2016 #8

    haruspex

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    Your calculation looks right to me.
     
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