# Finding radius of nucleus from semi-empirical mass formula?

1. Nov 25, 2012

### Collisionman

1. The problem statement, all variables and given/known data

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.

2. Relevant 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: $R=R_{0}A^{\frac{1}{3}}$

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. Dec 9, 2012

### Collisionman

I'm bumping this question up.

Any help greatly appreciated.

Thanks.