When potassium permanganate $(KMnO_4)$ is heated at $513 \ K$,it decomposes to form two manganese-based products. The physical properties of the product in which manganese has a higher oxidation state than the other are:

$A$ first row transition metal with the highest enthalpy of atomization,upon reaction with oxygen at high temperature,forms oxides of the formula $M_2O_n$ (where $n=3, 4, 5$). The 'spin-only' magnetic moment value of the amphoteric oxide from the above oxides is $......$ $BM$ (nearest integer). (Given atomic number: $Sc: 21, Ti: 22, V: 23, Cr: 24, Mn: 25, Fe: 26, Co: 27, Ni: 28, Cu: 29, Zn: 30$)

$A$ purple colored compound of Manganese $(X)$ decomposes on heating to liberate oxygen and forms compounds of Manganese $(Y)$ and $(Z)$. Compound $(Z)$ reacts with $KOH$ in the presence of potassium nitrate to give compound $(Y)$. Compounds $(X)$,$(Y)$,and $(Z)$ respectively are:

Fill in the blanks:
$(a)$ The unit of magnetic moment is ......... .
$(b)$ $Mn^{2+}$ has .......... color.
$(c)$ $Fe_3H$ is a ............. type of compound.

Which of the following imparts green colour to the glass?

Consider the following chemical reactions involved in the extraction of chromium from chromite ore:
$(a)$ $4FeCr_2O_4 + X_1 + 7O_2 \to 8Na_2CrO_4 + 2Fe_2O_3 + 8CO_2$
$(b)$ $2Na_2CrO_4 + X_2 \to Na_2Cr_2O_7 + 2Na^+ + H_2O$
Identify the species $X_1$ and $X_2$ in the reactions.