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What happens when a mixture of cobalt oxide and borax is heated in a flame on a loop of platinum wire?
(A) A transparent white bead is formed
(B) A bright pink coloured $NaB{{O}_{2}}$ bead is formed
(C) A blue coloured $Co{{(B{{O}_{2}})}_{2}}$ bead is formed
(D) A red coloured $Co{{(B{{O}_{2}})}_{2}}$ bead is formed

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Hint: Certain important trends are observed in the chemical behavior of group 13 elements. Especially Boron forms some important compounds which are very useful chemical properties. The compounds of boron are borax, orthoboric acid, diborane, and some borohydrides.

Complete step by step answer:
Borax is the most important compound of boron. The chemical formula of Borax is $N{{a}_{2}}{{B}_{4}}{{O}_{7}}.10{{H}_{2}}O$ and it is a white crystalline solid. Tetranuclear units ${{[{{B}_{4}}{{O}_{5}}{{(OH)}_{4}}]}^{2-}}$ contain in the crystalline state, then the formula is $N{{a}_{2}}[{{B}_{4}}{{O}_{5}}{{(OH)}_{4}}].8{{H}_{2}}O$

On heating, borax gets fused and loses water of crystallization. It swells up into a white porous mass and then melts into a colorless liquid which forms a clear transparent glass bead. This bead consists of boric anhydride (${{B}_{2}}{{O}_{3}}$) and sodium metaborate.
$N{{a}_{2}}{{B}_{4}}{{O}_{7}}.10{{H}_{2}}O\overset{\Delta }{\mathop{\to }}\,N{{a}_{2}}{{B}_{4}}{{O}_{7}}\to 2NaB{{O}_{2}}+{{B}_{2}}{{O}_{3}}$

When boric anhydride is heated with a colored metallic salt, a characteristic colored bead of metal metaborate is formed, because boric anhydride is non-volatile.
Thus, when reacted with cobalt oxide forms blue colored $Co{{(B{{O}_{2}})}_{2}}$ beads.
${{B}_{2}}{{O}_{3}}+CoO\to Co{{(B{{O}_{2}})}_{2}}$

Hence, when a mixture of cobalt oxide and borax is heated in a flame on a loop of platinum wire a blue colored $Co{{(B{{O}_{2}})}_{2}}$ bead is formed.
So, the correct answer is “Option C”.

Note: Borax bead test means a small loop of a platinum wire heated on a Bunsen burner flame until red hot. This test is used for inorganic qualitative analysis for the presence of certain metals. Characteristic color beds are formed with the salts of copper, iron, chromium, magnesium, cobalt, and nickel.