Salt `A+SrarrBoverset(BaCl_(2))rarr` White precipitate A is paramagnetic in nature and contains about 55% K. Thus, A is

Options

A. 9
B. 12
C. 27
D. 81

Answer

3

Explanation

Let consider a tetrahedron with vertices
`O(0,0,0),A(a,0,0),B(0,b,0)&C(0,0,c)`its
volume `(V) =(1)/(6)[veca" "vecb" "vecc]=(1)/(6)[bar(OA)" "bar(OB)" "bar(OC)]`
Now , centroids of the faces OAB,OAC,,OBC&
`ABC are G_(1)((a)/(3),(b)/(3),0),G_(2)((a)/(3),0,(c)/(3)),G_(3) (0,(b)/(3),(c)/(3))&G_(4)((a)/(3),(b)/(3),(c)/(3))` respectively
`then bar(G_(4)G_(1))=((veca)/(3)),bar(G_(4)G_(2))=((vecb)/(3))& bar(G_(4)G_(3))=(veca)/(3)`
Volume of trtrhedron by centroids
`V'=(1)/(6)[bar(G_(4)G_(1))" "bar(G_(4)G_(2))" "bar(G_(4)G_(3))]=(1)/(6)[(vec(a))/(3)(vecb)/(3)(vecc)/(3)]`
`=(1)/(27)Vimpliesk=27`