To determine the correctness of the given statements, we need to analyze each one individually:
Statement I: "Colourless cupric metaborate is reduced to cuprous metaborate in a luminous flame."
- Cupric metaborate (\(\text{Cu(BO}_2\)_2\)) is a compound that contains copper in the +2 oxidation state (\(\text{Cu}^{2+}\)).
- A luminous flame is a flame that provides both heat and light, typically featuring yellow or bright colors, often resulting from incomplete combustion.
- Reduction typically involves the gain of electrons, which would reduce the oxidation state of copper from +2 (cupric) to +1 (cuprous, \(\text{Cu}^{+}\)).
- However, in practice, the reduction of cupric metaborate to cuprous metaborate would not occur simply in a luminous flame without specific reducing conditions or reducing agents.
Therefore, Statement I is false.
Statement II: "Cuprous metaborate is obtained by heating boric anhydride and copper sulphate in a non-luminous flame."
- Boric anhydride (\(\text{B}_2\text{O}_3\)) and copper sulfate (\(\text{CuSO}_4\)) are the starting materials mentioned.
- A non-luminous flame is typically a blue-colored flame resulting from the complete combustion, providing only heat without light.
- Cuprous compounds, generally containing copper in the +1 oxidation state, are less common and require specific conditions for their formation.
- The reaction conditions described do not typically result in the formation of cuprous metaborate. The expected product under such conditions would likely include oxide salts or different borate formations, but not cuprous metaborate directly from these reactants in a simple heating process.
Therefore, Statement II is false.
Given the analysis above, the most appropriate answer is that both Statement I and Statement II are false.