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Finding radius of nucleus from semi-empirical mass formula?

  1. Nov 25, 2012 #1
    1. The problem statement, all variables and given/known data

    The nuclei [itex]^{41}_{21}Sc[/itex] and [itex]^{41}_{20}Ca[/itex] are said to be a pair of mirror nuclei. If the binding energy of [itex]^{41}_{21}Sc[/itex] and [itex]^{41}_{20}Ca[/itex] is [itex]343.143 MeV[/itex] and [itex]350.420 MeV[/itex], respectively, estimate the radii of the two nuclei with the aid of the Semi-Empirical Mass Formula.

    2. Relevant equations

    1. Semi-Empirical Mass Formula: [itex]M_{Z,A} = Zm_{p} + Zm_{e}[/itex][itex] + \left(A-Z\right)m_{n} -a_{volume}A + a_{surface}A^{\frac{2}{3}}[/itex][itex] + a_{coulomb}\frac{Z\left(Z-1\right)}{A^{\frac{1}{3}}}[/itex][itex] + a_{asymmetry}\frac{\left(A-2Z\right)^{2}}{A} + \delta[/itex]
    2. Binding Energy: [itex]E_{b} = a_{volume}A - a_{surface}A^{\frac{2}{3}}[/itex][itex] - a_{coulomb}\frac{Z\left(Z-1\right)}{A^{\frac{1}{3}}}[/itex][itex] - a_{asymmetry}\frac{\left(A-2Z\right)^{2}}{A} - \delta[/itex]
    3. Radius of a nucleus: [itex]R=R_{0}A^{\frac{1}{3}}[/itex]

    3. The attempt at a solution

    I don't know exactly where to start with this question. I'm not quite sure how to relate the nuclear radius to the SEMF.

    Anyway hints/help would be greatly appreciated.

    Thanks!
     
  2. jcsd
  3. Dec 9, 2012 #2
    I'm bumping this question up.

    Any help greatly appreciated.

    Thanks.
     
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