The question provides two statements related to the chemistry of manganese compounds, and we need to determine the veracity of these statements based on chemical reactions and principles.
Statement I: Fusion of \(MnO_2\) with \(KOH\) and an oxidising agent gives dark green \(K_2MnO_4\).
Explanation: When manganese dioxide (\(MnO_2\)) is fused with potassium hydroxide (\(KOH\)) in the presence of an oxidizing agent such as chlorine (\(Cl_2\)) or potassium nitrate (\(KNO_3\)), it forms potassium manganate (\(K_2MnO_4\)), which is dark green.
This reaction can be represented as: \(2MnO_2 + 4KOH + O_2 \rightarrow 2K_2MnO_4 + 2H_2O\)
Therefore, Statement I is true.
Statement II: Manganate ion on electrolytic oxidation in alkaline medium gives permanganate ion.
Explanation: In alkaline medium, the manganate ion (\(MnO_4^{2-}\)) can undergo further oxidation to form permanganate ion (\(MnO_4^{-}\)), especially under electrolytic conditions. This transformation occurs due to the gain of an electron by \(MnO_4^{2-}\):
\(MnO_4^{2-} \ + \ e^- + \ H_2O \rightarrow \ MnO_4^- + 2OH^-\)
This shows an increase in oxidation state from Mn (+6 in manganate) to Mn (+7 in permanganate).
Hence, Statement II is also true.
Conclusion: Based on the explanations, both Statement I and Statement II are true. Therefore, the correct answer is: Both Statement I and Statement II is true.
Statement I: True. Fusion of MnO$_2$ with KOH in the presence of oxygen gives K$_2$MnO$_4$ (potassium manganate), which is dark green in color: \[ \text{MnO}_2 + 4\text{KOH} + \text{O}_2 \xrightarrow{\text{fusion}} 2\text{K}_2\text{MnO}_4 + 2\text{H}_2\text{O}. \]
Statement II: True. In alkaline medium, the manganate ion (MnO$_4^{2-}$) undergoes electrolytic oxidation to form the permanganate ion (MnO$_4^-$): \[ \text{MnO}_4^{2-} \rightarrow \text{MnO}_4^- + e^-. \]
Both statements are correct as they describe valid chemical processes.
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)

Cobalt chloride when dissolved in water forms pink colored complex $X$ which has octahedral geometry. This solution on treating with cone $HCl$ forms deep blue complex, $\underline{Y}$ which has a $\underline{Z}$ geometry $X, Y$ and $Z$, respectively, are
Cobalt chloride when dissolved in water forms pink colored complex $X$ which has octahedral geometry. This solution on treating with cone $HCl$ forms deep blue complex, $\underline{Y}$ which has a $\underline{Z}$ geometry $X, Y$ and $Z$, respectively, are
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,