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When fused lead bromide is electrolysed, we observe:
A. silver-grey deposit at anode and a reddish-brown, deposit at cathode
B. A silver-grey deposit at cathode and a reddish-brown, deposit at anode
C. A silver-grey deposit at cathode and a reddish-brown fumes at anode
D. A silver-grey fumes at anode and a reddish-brown fumes at cathode

Answer
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Hint: Electrolysis involves the use of electricity to break down electrolytes to give elements. In this process the negative ion moves towards the anode and vice versa. Fused lead bromide ( lead in the heated liquid state) while undergoing electrolysis gets electrolyzed by the following process and the components get deposited at the respective electrodes.

Complete step by step answer:
Fused lead bromide undergoes electrolysis which means splitting of ions using electrical energy and movement to ions to respective electrodes.
During the electrolysis process, $P{b^{2 + }}$ ions gain electrons at the cathode and become Pb atoms. Similarly, $B{r^ - }$ ions lose electrons at the cathode and become Br atoms that pair up to form $B{r_2}$ molecules. Vapors of bromine gas are formed and it is reddish-brown. It is liberated at the anode. So reddish-brown fumes are deposited at the anode.
At cathode silver-grey deposit of lead is seen. The reactions taking place at the respective electrodes are as follows

$P{b^{2 + }} + 2{e^ - } \to Pb$

$B{r^ - } - e \to Br$

Now this bromine atom combines to form a bromine molecule.
Therefore a silver-grey deposit at the cathode and brown fumes at the anode are observed.

So, the correct answer is Option C .

Note: Solid lead bromide is unable to conduct electricity at normal temperatures and the temperature has to be at around ${370^ \circ }$ C. Molten lead bromide is taken for electrolysis process as for electrolysis process the ions has to be free to move that is possible in molten state or an aqueous solution and pure lead bromide has a relatively low melting point. Also, it is a type of decomposition reaction since lead bromide breaks into two parts that are Pb and Br.