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Find the unknown isotope.

  1. Apr 29, 2009 #1
    1. The problem statement, all variables and given/known data

    A particular isotope of dysprosium has atomic number 66 and atomic mass 159.952202 u. Identify the nucleus with a radius that is one half that of this isotope.

    A. Ne (A=20, Z=10) <<<Correct Answer
    B. O (A=16, Z=8)
    C. Mn (A=50, Z=25)
    D. Ni (A=60, Z=28)

    2. Relevant equations
    The only relevant equation I can think of is the equation of a nucleus's radius in terms of its atomic number:

    r = (1.2X10^-15)(A^[1/3])

    3. The attempt at a solution

    My attempt has gone as follows:

    1. Find the radius of the given dysprosium isotope by plugging it's atomic number into the given formula:

    r1 = (1.2X10^-15)(66^[1/3])
    r1 = 4.849488E-15 m

    2. Now I find the radius of the unknown nucleus:

    r2 = (1/2)r1
    r2 = 2.424744E-15 m

    3. Finally, by plugging the r2 value into the original equation, I should be able to solve for the atomic number of the unknown nucleus:

    r2 = 2.424744E-15 m = (1.2X10^-15)(A2^[1/3])

    A2 = 8.25

    This is obviously not correct, it seems I'm missing a step; possibly one involving the atomic mass, since it is mentioned in the problem. Any help would be appreciated.

    Thanks!
     
  2. jcsd
  3. Apr 29, 2009 #2

    rl.bhat

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    Homework Helper

    r1 = (1.2X10^-15)(66^[1/3])
    This is wrong. A is atomic mass, not atomic number.
     
  4. Apr 29, 2009 #3
    Ahhhhhh, of course. Thanks again rl.bhat!
     
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