[ centres. (a) Using an infinite square well model demonstrate from first principles that the eigenvalues of a particle in a three dimensional box of side d are En = h212 2md 2 ( notny + n2 ), where nix,y,z are integers. [4] (b) Given the lattice parameter do - 6.29 A for KCI and the energy levels described in the equation above, calculate the energy of its colour centre (F-centre). E= = 2.85 QV [3.5] (c) If the atoms surrounding the F-centre vibrate with an rms displacement amplitude of about ao/10, use the square well model to estimate the linewidth of the absorption band in the spectrum. AE = 0.87 ev [3.5]