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The hydrogen-like species \(\mathrm{Li}^{2+}\) is in a spherically symmetric state \(S_1\) with one radial node. Upon absorbing light the ion undergoes transition to a state \(S_2\). The state \(S_2\) has one radial node and its energy is equal to the ground state energy of the hydrogen atom.
Question:
The state \(S_1\) is

Extraction of copper from copper pyrite $\left(\mathrm{C}\mathrm{u}\mathrm{F}\mathrm{e}{\mathrm{S}}_2\right)$ involves

The compound(s) with \(\mathrm{P}-\mathrm{H}\) bond(s) is(are)

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The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.
The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers \(+2,+4\) and \(+6 . \mathrm{XeF}_4\) reacts violently with water to give \(\mathrm{XeO}_3\). The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.
Question:
The structure of \(\mathrm{XeO}_3\) is

For the following reaction, the equilibrium constant ${\mathrm{K}}_{\mathrm{e}}$ at $298\mathrm{ }\mathrm{K}$ is $1.6\times {10}^{17}.$
$\mathrm{F}{\mathrm{e}}^{2+}\left(\mathrm{a}\mathrm{q}\right)+{\mathrm{S}}^{2-}\left(\mathrm{a}\mathrm{q}\right)\mathrm{ }\rightleftharpoons \mathrm{F}\mathrm{e}\mathrm{S}\left(\mathrm{s}\right)$
When equal volumes of $0.06\mathrm{ }\mathrm{M}\mathrm{ }\mathrm{F}{\mathrm{e}}^{2+}\left(\mathrm{a}\mathrm{q}\right)$ and $0.2\mathrm{ }\mathrm{M}{\mathrm{ }\mathrm{S}}^{2-}\left(\mathrm{a}\mathrm{q}\right)$ solutions are mixed, the equilibrium concentration of $\mathrm{F}{\mathrm{e}}^{2+}\left(\mathrm{a}\mathrm{q}\right)$ is found to be $\mathrm{Y}\times {10}^{-17}\mathrm{M}.$ The value of $\mathrm{Y}$ is __________

An organic compound undergoes first-order decomposition. The time taken for its decomposition to \(1 /\) 8 and \(1 / 10\) of its initial concentration are \(t_{1 / 8}\) and \(t_{1 / 10}\) respectively. What is the value of \(\left[\frac{t_{1 / 8}}{t_{1 / 10}}\right] \times 10\) ? \(\left(\log _{10} 2=0.3\right)\)

The work function ( \(\Phi\) ) of some metals is listed below. The number of metals which will show photoelectric effect when light of \(300 \mathrm{~nm}\) wavelength falls on the metal is

Most materials have the refractive index, \(n>1\). So, when a light ray from air enters a naturally occurring material, then by Snell's

law, \(\frac{\sin \theta_{1}}{\sin \theta_{2}}=\frac{n_{2}}{n_{1}}\), it is understood that the refracted ray bends towards the normal. But it never emerges on the same side of the normal as the incident ray. According to electromagnetism, the refractive index of the medium is given by the relation, \(\mathrm{n}=c / v=\pm \sqrt{\varepsilon_{r} \mu_{r}}\), where \(c\) is the speed of electromagnetic waves in vacuum, \(v\) its speed in the medium, \(\varepsilon_{r}\) and \(\mu_{r}\) are the relative permittivity and permeability of the medium respectively. In normal materials, both \(\varepsilon_{r}\) and \(\mu_{r}\), are positive, implying positive \(n\) for the medium. When both \(\varepsilon_{r}\) and \(\mu_{r}\) are negative, one must choose the negative root of \(n\). Such negative refractive index materials can now be artificially prepared and are called metamaterials. They exhibit significantly different optical behavior, without violating any physical laws. Since \(n\) is negative, it results in a change in the direction of propagation of the refracted light. However, similar to normal materials, the frequency of light remains unchanged upon refraction even in meta-materials.
Question : Choose the correct statement.

At \(25^{\circ} \mathrm{C}\), the concentration of \(\mathrm{H}^{+}\)ions in \(1.00 \times 10^{-3} \mathrm{M}\) aqueous solution of a weak monobasic acid having acid dissociation constant \(\left(K_a\right)=4.00 \times 10^{-11}\) is \(\boldsymbol{X} \times 10^{-7} \mathrm{M}\). The value of \(\boldsymbol{X}\) is _____ .
Use: Ionic product of water \(\left(K_w\right)=1.00 \times 10^{-14}\) at \(25^{\circ} \mathrm{C}\)

In the following \([x]\) denotes the greatest integer less than or equal to \(x\). Match the functions in Column I with the properties Column II.

The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is (are)

Consider an elliptically shaped rail PQ in the vertical plane with $\mathrm{O}\mathrm{P}\mathrm{}=\mathrm{}3\mathrm{}\mathrm{m}$ and $\mathrm{O}\mathrm{Q}\mathrm{}=\mathrm{}4\mathrm{}\mathrm{m}$ . A block of mass 1 kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is $(\mathrm{n}\times 10)$ Joules. The value of n is (take acceleration due to gravity = $10\mathrm{}\mathrm{m}{\mathrm{s}}^{–2}$ )

In the figure below, the switches $S_1\mathrm{a}\mathrm{n}\mathrm{d}{S}_2$ are closed simultaneously at $t=0$ and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current I in the middle wire reaches its maximum magnitude $I_{max}$ time $t=\tau$. Which of the following statements is (are) true?