# Electron scattering: nuclear radius to nucleon number relationship

Hi! I am extremely confused on what seems to be quite a simple question. The question contains a graph of root mean square radius <r$^{2}$> plotted against A$^{1/3}$ where A is the nucleon number. In the lecture notes he specifies that <r$^{2}$> is not the same as R but does not really say specifically what the difference is. It is given that the gradient of the line in this graph is 0.96. I am meant to find the value of R$_{0}$ in the relationship R=R$_{0}$A$^{1/3}$ but I'm not certain how to find it because I dont know what the relationship between the rms r and R is.

Any help would be amazing.

I have worked through trying to use the charge radius but without success, he never mentioned the charge radius in the lecture so I'm not sure what to do. http://en.wikipedia.org/wiki/Charge_radius

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• PC3232_assignment_2_1314s1.pdf
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mfb
Mentor
If you have a uniform sphere of radius R, what is the (squared) rms radius <r2> of its volume? Hint: You'll need an integral (or a formula).

• 1 person
Thanks so much I think I'm on the right track now. So for a uniform sphere you use some spherical coordinate integrals to find that the rms radius is related to the radius by $\frac{3}{5}$R$^{2}$. Is this the correct formula to get?

Also am I right in saying that I am effectively finding the expectation value of r$^{2}$?

Finally got the answer! Thanks again man couldn't have done it without you!

vela
Staff Emeritus
Thanks so much I think I'm on the right track now. So for a uniform sphere you use some spherical coordinate integrals to find that the rms radius is related to the radius by $\frac{3}{5}$R$^{2}$. Is this the correct formula to get?
Also am I right in saying that I am effectively finding the expectation value of r$^{2}$?