Give the balanced equation for the conversion of argentite ( $A{g_2}S$ ) to metallic silver.

Hint: Metals exist in the environment in free or the combined state. Some metals like gold or platinum are inert and thus exist in the metallic form, others exist in the combined form as ores. Ores are the impure form of the metals which need to be purified to obtain the actual metals.

Complete step by step answer:
Most metals exist in nature combined in the form of ores from which we need to take out the needed metals. There can be many more metals and their abundance in nature defines the effort and cost that needs to be put into obtaining the metal. The ore from which the extraction of the metal is the most feasible is used for commercial purposes.
Argentite is one such ore for the metal silver. For obtaining pure silver we need to treat the ore through various processes. Argentite is treated with $0.5\% $ sodium cyanide solution in the presence of air to form a complex. This complex is soluble. The reactions involved in the process can be depicted as
$A{g_2}S + 2NaCN \rightleftharpoons N{a_2}S + 2AgCN \downarrow $
$AgCN + NaCN\xrightarrow[{}]{}Na[Ag{(CN)_2}]$
To the precipitate silver, the zinc dust is added. Zinc is more electropositive than silver.
$2Na[Ag{(CN)_2}] + Zn\xrightarrow[{}]{}N{a_2}[Zn{(CN)_4}] + 2Ag \downarrow $
Or the reaction can be also be as,
$2Na[Ag{(CN)_2}] + 4NaOH + Zn\xrightarrow{{}}N{a_2}Zn{O_2} + 4NaCN + 2{H_2}O + 2Ag \downarrow $
In both the upper reactions the silver metal is precipitated.

Note: Some various procedures and steps need to be followed for the extraction process to occur. This process involves treating the ore and making it ready for any chemical process to be carried out. The ore is extracted and is impure in the form of rocks which need to be broken and pulverized before it is treated by the chemicals for the extraction of the metals.