We wish to observe an object which is $2.5 \mathrm{Å}$ in size. The minimum energy photon that can be used is

For scattering to occur, the wavelength of the waves must be of the same order of magnitude or smaller than the size of the object being observed. Hence, the largest possible wavelength we can use in the present problem is ${\lambda }_{max}=2.5 \mathrm{Å}$. Hence, minimum energy is

$E_{min}=h{v}_{min}=\frac{hc}{{\lambda }_{max}}=\frac{12.40\times {10}^3 \mathrm{eV}.\mathrm{Å}}{2.5 \mathrm{Å}}=5 \mathrm{keV}$