For an element to emit characteristic X-rays from its K-shell, an electron from the outer shell of the atom must be incident on the atom with sufficient energy to eject an electron from the K-shell. The ejected electron leaves a vacancy, and when another electron from a higher energy level falls into this vacancy, X-rays are emitted. This phenomenon is known as characteristic X-ray emission.
In order for this process to occur, the incident energy must be greater than the corresponding ionization potential of the K-shell. The ionization potential refers to the energy required to remove an electron from the K-shell. If the energy is less than this value, the electron in the K-shell will not be ejected, and no characteristic X-rays will be emitted.
Therefore, the correct condition for the emission of characteristic X-rays is that the incident energy must be greater than the ionization energy of the K-shell, which enables the removal of the electron from the shell.
In contrast, the bond energy or the binding energy of electrons in other shells is irrelevant in this context because it is the K-shell's ionization energy that governs the threshold for X-ray emission.