No, it is not possible to use gamma rays to knock inner electrons of an atom into a higher energy level or shell. Gamma rays are high-energy photons, but they do not possess the specific energy levels required to promote electrons from lower energy levels to higher ones.
Electron transitions between energy levels within an atom typically occur through the absorption or emission of photons with specific energies corresponding to the energy difference between the levels involved. Gamma rays, with their high energy, are typically involved in interactions with atomic nuclei rather than electrons.
In the case of beryllium (Be), which has an atomic number of 4, it has two inner electrons in the first shell and two outer electrons in the second shell. The electron configuration of beryllium is 1s^2 2s^2. To excite the electrons in beryllium, one would need to provide energy corresponding to the specific energy difference between the relevant energy levels, typically through the absorption of photons within the ultraviolet or X-ray range, not gamma rays.
Gamma rays can interact with atoms and cause ionization by removing electrons from the outermost shells, but they do not directly cause transitions of electrons to higher energy levels within the atom.