Carbon Potential

If the electric potential inside a carbon atom can be expressed as

$V(r) = \frac{Ze}{a\pi {\epsilon}_{0}} \left(\frac{1}{r} - \frac{b}{cR} + \frac{{r}^{2}}{d{R}^{3}}\right)$

where $$R$$ is the radius of the carbon atom, calculate $$Z+a+b+c+d$$.

Notes

1) $$e$$ is the charge of a proton

2) $${\epsilon}_{0}$$ is the permittivity of free space

3) $$V(r)$$ should not be confused with the potential energy, which would be of the form $U(r) = -\frac{Z{e}^{2}}{a\pi {\epsilon}_{0}} \left(\frac{1}{r} - \frac{b}{cR} + \frac{{r}^{2}}{d{R}^{3}}\right)$

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