Finding radius of nucleus from semi-empirical mass formula?

In summary, to estimate the radii of the mirror nuclei ^{41}_{21}Sc and ^{41}_{20}Ca using the Semi-Empirical Mass Formula, we can use the formula for binding energy and the formula for nuclear radius. The nuclear radius can be calculated using the value of R_{0} and the mass number A. Further assistance may be needed to fully solve this problem.
  • #1
Collisionman
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Homework Statement



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.

Homework 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]

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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  • #2
I'm bumping this question up.

Any help greatly appreciated.

Thanks.
 

Related to Finding radius of nucleus from semi-empirical mass formula?

1. What is the semi-empirical mass formula?

The semi-empirical mass formula is a mathematical formula used to calculate the approximate mass of an atomic nucleus based on the number of protons and neutrons it contains. It takes into account the strong nuclear force, the Coulomb force, and the asymmetry energy of the nucleus.

2. How is the radius of a nucleus calculated using the semi-empirical mass formula?

The radius of a nucleus can be calculated using the semi-empirical mass formula by first calculating the binding energy of the nucleus. The radius can then be determined by using the relation between binding energy and nuclear radius, which is based on the liquid drop model of the nucleus.

3. What factors affect the radius of a nucleus according to the semi-empirical mass formula?

The radius of a nucleus is affected by several factors according to the semi-empirical mass formula. These include the mass number, the number of protons and neutrons, the nuclear binding energy, and the asymmetry energy of the nucleus.

4. Is the semi-empirical mass formula accurate in predicting the radius of a nucleus?

The semi-empirical mass formula is an approximate method for calculating the radius of a nucleus. It takes into account the most important factors that contribute to the nuclear binding energy and therefore, it provides a reasonably accurate prediction of the nuclear radius.

5. How does the semi-empirical mass formula compare to other methods for determining the radius of a nucleus?

Compared to other methods for determining the radius of a nucleus, the semi-empirical mass formula is relatively simple and provides a good estimate of the nuclear radius. However, more accurate methods such as the shell model or the liquid drop model can also be used, depending on the specific characteristics of the nucleus in question.

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