The reagent used for the identification of ammonium cation in the analysis of a simple salt is:
  A.\;\;\;\;\;KI \\
  B.\;\;\;\;\;{K_2}Hg{I_4} \\
  C.\;\;\;\;\;{K_2}Cr{O_4} \\
  D.\;\;\;\;\;{K_4}\left[ {Fe{{\left( {CN} \right)}_6}} \right] \\

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  Reagents are used in a chemical reaction to detect, measure, or make other substances. Ammonium ions can be identified in a solution by adding dilute sodium hydroxide solution and gently heating. If ammonium ions are present they will convert to ammonia gas.

Complete step by step answer:
-The ammonia gas formed by the reaction of ammonium ions with NaOH reacts with Nessler’s reagent to form a brown precipitate of H2N, HgO, HgI
$2{K_2}\left[ {Hg{I_4}} \right] + N{H_3} + 3KOH \to {H_2}N.HgO.HgI + 7KI + 2{H_2}O$\[\]
\[{K_2}{\left[ {HgI} \right]_4}\] is an organic compound consisting of a potassium cation and the tetraiodomercurate(II) anion. It is mainly used as nessler’s reagent, used to detect ammonia.
-It is an aqueous solution of potassium iodide, mercuric chloride, and potassium hydroxide.
Ammonium ion is formed by the reaction between acids and aqueous ammonia. The ammonium ion behaves chemically like the ions of the alkali metals, particularly potassium ion, which is almost the same size. All ammonium salts are white and soluble.

Hence option B is correct.

Additional information:
-Exposure of high concentrations of ammonia in air causes immediate burning of eyes, nose, throat, and respiratory tract and can result in blindness, lung damage or death.
-Inhalation of lower concentrations can cause coughing, and nose and throat irritation.
-Anhydrous ammonia is compressed into a clear colorless liquid when used as a fertilizer. If you inhale it and it gets in your windpipe and your lungs, it will cause burns and may these may be fatal.

 The positively charged H+ ion, or proton, is attracted to lone pairs at the negative end of ammonia dipole. The crucial difference is that the ammonium ion has one more proton in the nucleus of the central atom and hence overall charge of +1 ( hence, a positive ion).