No, it is not possible to use gamma rays to directly knock the inner electrons of an atom into a higher energy level or shell. Gamma rays, which are high-energy photons, interact with atomic electrons through processes like photoelectric effect, Compton scattering, and pair production, but these interactions typically involve the outermost electrons or the nucleus of the atom.
In the case of beryllium (Be), it has four electrons arranged in two energy levels: two in the first energy level (K shell) and two in the second energy level (L shell). The innermost electrons in the K shell are tightly bound to the nucleus and require much higher energy interactions, such as X-rays or high-energy particles, to be ionized or excited to higher energy levels.
Gamma rays, being even more energetic than X-rays, can ionize the atoms by removing electrons from the outermost energy levels, including the L shell in the case of beryllium. These ionizations can lead to the production of free electrons or the creation of vacancies in the electron shells, which may subsequently lead to cascades of electron transitions as the atom stabilizes.
However, directly knocking the inner electrons of beryllium into a higher energy level using gamma rays is not a typical process. The energy required to excite or ionize inner electrons is significantly higher than what gamma rays can generally provide. The interactions of gamma rays with matter are more commonly associated with outer-shell electrons or the atomic nucleus.
It's worth noting that the behavior of atoms and their electrons is described by quantum mechanics, which entails probabilistic nature and discrete energy levels. Electron transitions within an atom generally occur through absorption or emission of photons that possess specific energies corresponding to the energy differences between the involved energy levels.