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
Given below are two statements:
Statement I: In the oxalic acid vs KMnO$_4$ (in the presence of dil H$_2$SO$_4$) titration the solution needs to be heated initially to 60°C, but no heating is required in Ferrous ammonium sulphate (FAS) vs KMnO$_4$ titration (in the presence of dil H$_2$SO$_4$).
Statement II: In oxalic acid vs KMnO$_4$ titration, the initial formation of MnSO$_4$ takes place at high temperature, which then acts as catalyst for further reaction. In the case of FAS vs KMnO$_4$, heating oxidizes Fe$^{2+}$ into Fe$^{3+}$ by oxygen of air and error may be introduced in the experiment.
In the light of the above statements, choose the correct answer from the options given below:
Given below are two statements:
Statement I: In the oxalic acid vs KMnO$_4$ (in the presence of dil H$_2$SO$_4$) titration the solution needs to be heated initially to 60°C, but no heating is required in Ferrous ammonium sulphate (FAS) vs KMnO$_4$ titration (in the presence of dil H$_2$SO$_4$).
Statement II: In oxalic acid vs KMnO$_4$ titration, the initial formation of MnSO$_4$ takes place at high temperature, which then acts as catalyst for further reaction. In the case of FAS vs KMnO$_4$, heating oxidizes Fe$^{2+}$ into Fe$^{3+}$ by oxygen of air and error may be introduced in the experiment.
In the light of the above statements, choose the correct answer from the options given below:
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,