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Intro physics proportion question

  1. Sep 5, 2013 #1
    1. The problem statement, all variables and given/known data

    The radius of a proton is roughly 10^-15m, while the radius of a hydrogen atom is about 0.5x10^-10m. If we were to enlarge both proportionally until the proton was as large as a marble, about how large would the atom be?

    2. Relevant equations



    3. The attempt at a solution

    I calculated an answer of 300m, but this doesn't seem correct for the size of a Hydrogen atom. I simply took the radius of a marble to be approximately 0.6cm, found the proton had to increase by 6x10^12 to become the size of the marble and multiplied this increase factor by the radius of the hydrogen atom and got 300 :$
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 5, 2013 #2

    gneill

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    Staff: Mentor

    The proportion looks okay. The straightforward approach is to set up the ratios as an equation.

    $$\frac{r_{hydrogen}}{r_{proton}} = \frac{r_x}{r_{marble}}$$
     
  4. Sep 5, 2013 #3
    What is rx? I'd have (0.5x10^-10)/(10^-15)=rx/x? Assume the marble radius is x..
     
  5. Sep 5, 2013 #4

    gneill

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    Staff: Mentor

    ##r_x## is the unknown radius of the "inflated" atom.
     
  6. Sep 5, 2013 #5
    I guess my question is how would I use that ratio to show that the atom is always 50,000 times larger than proton?
     
  7. Sep 5, 2013 #6

    gneill

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    Staff: Mentor

    The ratio is a given. You have the radius of the proton, and the radius of the hydrogen atom. The rest is just proportional scaling (or comparison) of sizes.
     
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