(Solved): a and b Consider the hydrogen atom. The electric potential at a point P at a distance r from the nu ...

a and b

Consider the hydrogen atom. The electric potential at a point $$P$$ at a distance $$r$$ from the nucleus can be modelled as $$V(P)=\frac{1}{4?{?}_0}\frac{e}{r}\left(1+\frac{r}{a_0}\right)e^{?\frac{2r}{a_0}}$$ (a) What is the electric field created by the atom? (calculate at $$r>0$$ ) (b) Consider a sphere of radius $$R$$ around the nucleus. What is the charge inside this sphere? (Hint: Use Gauss' Law and the electric field you calculated in the previous part) (c) If you take the limit $$R?0$$, does the charge inside the sphere go to zero or takes a finite value? (d) How can you interpret the finite value that you obtained in the previous part? (e) If you take the limit $$R??$$, does the charge inside the sphere go to zero or takes a finite value? (is this atom neutral or not?)