Consider a very rough model of a beryllium atom. The nucleus...

By Gauss's law, the electric field at a distance $r$ from the center of a spherically symmetric charge distribution depends only on the net charge enclosed within a sphere of radius $r$.

For a point just inside the $1s$ cloud, the distance from the nucleus is $r = 1.3 \times 10^{-11} \text{ m}$. Since the point is just inside the electron cloud, the sphere of radius $r$ encloses only the nucleus. The electron clouds are outside this radius and do not contribute to the enclosed charge.

The beryllium nucleus contains $4$ protons, so the enclosed charge is $q = +4e = 4 \times 1.6 \times 10^{-19} \text{ C} = 6.4 \times 10^{-19} \text{ C}$.

The electric field is given by:

$E = \dfrac{1}{4\pi\epsilon_0} \dfrac{q}{r^2}$

Substituting the given values:

$E = \dfrac{9 \times 10^9 \times 6.4 \times 10^{-19}}{(1.3 \times 10^{-11})^2}$

$E = \dfrac{57.6 \times 10^{-10}}{1.69 \times 10^{-22}}$

$E \approx 34.1 \times 10^{12} \text{ N C}^{-1} = 3.4 \times 10^{13} \text{ N C}^{-1}$