The spin only magnetic moment of [ MnBr ₄ ]^ x - is 5.9 BM . The geometry of the complex and x respectively are

Step-by-step solution

_ s = n ( n +2) =5.9 B. M. ^2= n ( n +2)=34.81 n =5 Thus, Mn will have five unpaired electrons so Mn will be in +2 state with Br ⁻ being weak- field ligands. Thus, x=2 for [ Mn Br ₄ ]²⁻