For borax bead test:
• In the oxidizing flame, metal ions form metaborates, which produce characteristic colours.
• The observed colour is a key indicator of the specific metal ion present.
\(Cu(BO_2)_2\)
\(Cu_3B_2\)
Borax Bead Test:
1. Definition: The borax bead test is a qualitative test used to identify metal ions based on the colour imparted to the bead in the oxidizing or reducing flame.
In this test, borax (\(\text{Na}_2\text{B}_4\text{O}_7 \cdot 10\text{H}_2\text{O}\)) decomposes to form sodium metaborate (\(\text{NaBO}_2\)) and boric anhydride (\(\text{B}_2\text{O}_3\)) when heated:
\[\text{Na}_2\text{B}_4\text{O}_7 \xrightarrow{\Delta} 2\text{NaBO}_2 + \text{B}_2\text{O}_3.\]
2. Reaction with \(\text{CuSO}_4\): Copper ions react with boric anhydride (\(\text{B}_2\text{O}_3\)) to form copper metaborate (\(\text{Cu(BO}_2)_2\)) in the oxidizing flame:
\[\text{CuSO}_4 + \text{B}_2\text{O}_3 \rightarrow \text{Cu(BO}_2)_2 + \text{SO}_3.\]
3.Observation: \(\text{Cu(BO}_2)_2\) is responsible for the blue-green colour observed in the oxidizing flame.
Final Answer: \((3)\) \(\mathbf{Cu(BO}_2)_2\).
A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass = 300 g mol$^{-1}$) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $____________ \(\times 10^{-2}\). (nearest integer)
[Given : $K_{b}$ of the solvent = 5.0 K kg mol$^{-1}$]
Assume the solution to be dilute and no association or dissociation of X takes place in solution.
Inductance of a coil with \(10^4\) turns is \(10\,\text{mH}\) and it is connected to a DC source of \(10\,\text{V}\) with internal resistance \(10\,\Omega\). The energy density in the inductor when the current reaches \( \left(\frac{1}{e}\right) \) of its maximum value is \[ \alpha \pi \times \frac{1}{e^2}\ \text{J m}^{-3}. \] The value of \( \alpha \) is _________.
\[ (\mu_0 = 4\pi \times 10^{-7}\ \text{TmA}^{-1}) \]
A small block of mass \(m\) slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration \(a_0\). The angle between the inclined plane and ground is \(\theta\) and its base length is \(L\). Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is _______. 