91影视

$Ze$

We use Gauss' Law to find the electric field inside the sphere.

$桅=鈭�\stackrel{鈫�}{E}路\stackrel{鈫�}{da}=\frac{Q}{蔚0}$

Where

$桅$is the Electric Flux

E is the Electric Field

d a is the Area

Q is the Total Charge

$蔚$0 is the Permittivity

The charge inside the sphere from the electron can be evaluated as:

$Q=-Ze$

The total charge enclosed in a sphere of radius r is $\frac{-Ze{r}^3}{R^3}$

r is the radius inside the atom.

The electric field from the electrons can thus be given by:

$E\left(4蟺r^2\right)=\frac{-Ze{r}^3}{蔚0R^3}$

The electric field from nucleus is from a point charge Z e It is thus being given by:

$E\left(4蟺r^2\right)=\frac{Ze}{蔚0}$

Combining the above equations, we get:

$E=\frac{Ze}{4蟺蔚0}\left(\frac{1}{r^2}-\frac{r}{R^3}\right)$

Since atoms are neutral therefore it can be said that the electric field strength at the surface of the atom is 0

The electric field strength at the uranium surface is calculated as

$E=\frac{Ze}{4蟺蔚0}\left(\frac{1}{r^2}-\frac{r}{R^3}\right)$

Calculation:

Evaluating electric field for the values of

$\mathrm{Z}=92$, $\mathrm{R}=0.1$,$\mathrm{nm}$, r=0.5 R

$E=\frac{92脳1.6脳{10}^{-19}}{4蟺脳8.85脳{10}^{-12}}脳\left(\frac{1}{0.25脳0.1^2}-\frac{0.5}{0.1^2}\right)$

$=4.62脳{10}^{13}\mathrm{N}/\mathrm{C}$