Finding radius of nucleus from semi-empirical mass formula?

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SUMMARY

The discussion focuses on estimating the radii of the mirror nuclei ^{41}_{21}Sc and ^{41}_{20}Ca using the Semi-Empirical Mass Formula (SEMF). The binding energies provided are 343.143 MeV for Scandium and 350.420 MeV for Calcium. The relevant equations include the SEMF for mass and binding energy, as well as the formula for nuclear radius, R=R_{0}A^{\frac{1}{3}}. Participants seek guidance on how to effectively relate the nuclear radius to the SEMF in their calculations.

PREREQUISITES
  • Understanding of the Semi-Empirical Mass Formula (SEMF)
  • Knowledge of nuclear binding energy concepts
  • Familiarity with nuclear radius calculations
  • Basic proficiency in nuclear physics
NEXT STEPS
  • Study the derivation and application of the Semi-Empirical Mass Formula
  • Learn how to calculate binding energy using the SEMF
  • Research the constants used in the SEMF, such as a_{volume}, a_{surface}, a_{coulomb}, and a_{asymmetry}
  • Explore examples of calculating nuclear radii using R=R_{0}A^{\frac{1}{3}}
USEFUL FOR

Students and educators in nuclear physics, researchers analyzing nuclear properties, and anyone interested in the calculations related to nuclear structure and binding energy.

Collisionman
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Homework Statement



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

Homework Equations



  1. Semi-Empirical Mass Formula: M_{Z,A} = Zm_{p} + Zm_{e}+ \left(A-Z\right)m_{n} -a_{volume}A + a_{surface}A^{\frac{2}{3}}+ a_{coulomb}\frac{Z\left(Z-1\right)}{A^{\frac{1}{3}}}+ a_{asymmetry}\frac{\left(A-2Z\right)^{2}}{A} + \delta
  2. Binding Energy: E_{b} = a_{volume}A - a_{surface}A^{\frac{2}{3}}- a_{coulomb}\frac{Z\left(Z-1\right)}{A^{\frac{1}{3}}}- a_{asymmetry}\frac{\left(A-2Z\right)^{2}}{A} - \delta
  3. Radius of a nucleus: R=R_{0}A^{\frac{1}{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!
 
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I'm bumping this question up.

Any help greatly appreciated.

Thanks.
 

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