Question

{"given":"A $\\text{CsCl}$ crystal structure where we need to find the number of next nearest neighbours for a $\\text{Cs}^+$ ion.","key_observation":"In a $\\text{CsCl}$ crystal, $\\text{Cl}^-$ ions form a simple cubic lattice and $\\text{Cs}^+$ ions occupy the body-centered positions. The nearest neighbours of a $\\text{Cs}^+$ ion are $\\text{Cl}^-$ ions, and the next nearest neighbours are other $\\text{Cs}^+$ ions.","formula_steps":[],"option_analysis":[{"label":"(A)","text":"$12$","verdict":"incorrect","explanation":"$12$ is the number of next-next nearest neighbours, which are $\\text{Cs}^+$ ions at a distance of $\\sqrt{2}a$."},{"label":"(B)","text":"$8$","verdict":"incorrect","explanation":"$8$ is the number of nearest neighbours, which are $\\text{Cl}^-$ ions at a distance of $\\frac{\\sqrt{3}a}{2}$."},{"label":"(C)","text":"$6$","verdict":"correct","explanation":"$6$ is the number of next nearest neighbours, which are $\\text{Cs}^+$ ions located at the centers of adjacent unit cells at a distance of $a$."},{"label":"(D)","text":"$4$","verdict":"incorrect","explanation":"$4$ does not correspond to any of the primary coordination numbers in the $\\text{CsCl}$ lattice."}],"answer":"(C)"}