The energy of an electron in the \(n\)-th orbit of a hydrogen-like species is given by the Bohr formula: \(E_n = -13.6 \frac{Z^2}{n^2}\) eV.


For a doubly ionized Lithium atom (Li\(^{2+}\)), the atomic number \(Z = 3\).


The electron is in the ground state, so \(n = 1\).


Substituting the values into the formula: \(E_1 = -13.6 \times \frac{3^2}{1^2}\) eV.

\(E_1 = -13.6 \times 9 = -122.4\) eV.


The energy required to remove this electron (Ionization Energy) is the magnitude of the binding energy, which is \(+122.4\) eV.
Quick Tip: The ionization energy scales with \(Z^2\). For hydrogen (\(Z=1\)) it is 13.6 eV; for Li\(^{2+}\) (\(Z=3\)) it is \(13.6 \times 9\).

Xenon (Xe) has 8 valence electrons.


In XeF\(_4\), Xenon forms 4 sigma bonds with 4 Fluorine atoms, using 4 electrons.


The remaining valence electrons on Xenon are \(8 - 4 = 4\) electrons, which form 2 lone pairs.


The steric number (total electron domains) is the sum of sigma bonds and lone pairs: \(4 + 2 = 6\).


A steric number of 6 corresponds to \(sp^3d^2\) hybridization.


The geometry is octahedral, and the molecular shape is square planar.
Quick Tip: Formula for Steric Number: \(\frac{1}{2} (V + M - C + A)\). For XeF\(_4\): \(\frac{1}{2}(8 + 4 - 0 + 0) = 6 \rightarrow sp^3d^2\).

The spectrum of X-rays emitted from an X-ray tube consists of a continuous spectrum (Bremsstrahlung) and a characteristic spectrum.


When electrons strike the target, their kinetic energy is converted into photons. The maximum energy of a photon corresponds to the complete conversion of the electron's kinetic energy (\(eV\)).


Since energy is inversely proportional to wavelength (\(E = hc/\lambda\)), the maximum energy corresponds to a minimum wavelength (\(\lambda_{min}\)).

\(\lambda_{min} = \frac{hc}{eV}\).


No photon can have a wavelength shorter than this cutoff. Therefore, the beam contains wavelengths larger than this minimum limit.
Quick Tip: The "cutoff wavelength" (\(\lambda_{min}\)) depends inversely on the accelerating voltage (\(V\)). \(\lambda_{min} (\AA) \approx \frac{12400}{V (volts)}\).

Entropy (\(S\)) is a measure of disorder. The order of entropy is usually Gas \(>\) Liquid \(>\) Solid.


(A) Liquid \(\rightarrow\) Solid: Disorder decreases, so entropy decreases.


(B) Gas \(\rightarrow\) Liquid: Disorder decreases, so entropy decreases.


(C) Decomposition of NaHCO\(_3\): \(2NaHCO_3(s) \xrightarrow{\Delta} Na_2CO_3(s) + CO_2(g) + H_2O(g)\).


This reaction produces gaseous products from a solid reactant. The generation of gas significantly increases disorder.


Therefore, entropy increases in option (C).
Quick Tip: Look for the reaction where the number of moles of gaseous products is greater than the moles of gaseous reactants (\(\Delta n_g > 0\)).

In an electrochemical cell (both galvanic and electrolytic), the electrodes are defined by the reactions occurring at them.


The Anode is the electrode where oxidation (loss of electrons) takes place.


The Cathode is the electrode where reduction (gain of electrons) takes place.


Therefore, the reaction at the anode is oxidation.
Quick Tip: Remember the mnemonics: "An Ox" (Anode Oxidation) and "Red Cat" (Reduction Cathode).

For 1,2-disubstituted cyclohexanes, the relative positions (cis/trans) determine the conformational possibilities (axial/equatorial).


In the \textit{trans-1,2 isomer, the substituents are on opposite sides of the ring plane.


To maintain the trans relationship (dihedral angle approx 180\(^\circ\) or 60\(^\circ\) projection), the groups must be either both axial (\(a,a\)) or both equatorial (\(e,e\)).


The ring flip converts the diaxial conformer (\(1a, 2a\)) to the diequatorial conformer (\(1e, 2e\)).


The \textit{cis-1,2 isomer exists in (\(a,e\)) or (\(e,a\)) conformations.


Therefore, statements I (diaxial) and III (diequatorial) are correct for the trans isomer.
Quick Tip: For 1,2-substitution: Trans = aa or ee; Cis = ae or ea. Diequatorial is generally the most stable conformer.

Boiling point generally increases with molecular mass due to stronger Van der Waals forces.


Methanol (CH\(_3\)OH, Mass \(\approx\) 32) has a lower molecular mass than propyl alcohols (C\(_3\)H\(_7\)OH, Mass \(\approx\) 60). Thus, methanol has the lowest boiling point.


Between isomers, branching decreases the surface area, which weakens Van der Waals forces and lowers the boiling point.


n-propyl alcohol is a straight chain, while iso-propyl alcohol is branched.


Therefore, n-propyl alcohol has a higher boiling point than iso-propyl alcohol.


The correct order is: methanol \(<\) iso-propyl alcohol \(<\) n-propyl alcohol.
Quick Tip: Boiling Point Rules: 1. Increases with Molar Mass. 2. Decreases with Branching (for isomers).

The reaction of Grignard reagents (RMgX) varies with different substrates:


(A) Esters usually react with 2 equivalents of Grignard reagent to yield tertiary alcohols.


(B) Aldehydes yield secondary alcohols (Formaldehyde yields primary).


(C) Alkyl nitriles (R-CN) react with Grignard reagents to form an imine salt intermediate (\(R-C(R')=NMgX\)). Upon acid hydrolysis, this imine converts to a ketone (\(R-C(=O)-R'\)).


(D) Acid chlorides usually react with 2 equivalents to yield tertiary alcohols.


Therefore, alkyl nitriles are the correct substrate to produce ketones.
Quick Tip: Nitriles stop at the ketone stage because the intermediate formed is a stable imine salt that does not react further with Grignard reagent. Hydrolysis then releases the ketone.

Alkylbenzenes containing at least one benzylic hydrogen can be oxidized to benzoic acid by strong oxidizing agents.


Alkaline Potassium Permanganate (KMnO\(_4\)-KOH) followed by acidification is a standard reagent for this transformation.


Toluene (Methylbenzene) is oxidized directly to the benzoate ion, which gives Benzoic acid upon acidification.


Option (B) would require starting with a halobenzene, not toluene.


Option (C) oxidizes aldehydes.


Option (D) converts Toluene to Phenylacetic acid (adding an extra carbon).
Quick Tip: Side-chain oxidation of alkylbenzenes always yields Benzoic acid, regardless of the length of the alkyl chain, provided there is a benzylic hydrogen.

Insulin is a peptide hormone responsible for regulating blood glucose levels.


It is composed of two polypeptide chains connected by disulfide bridges.


Chain A consists of 21 amino acid residues.


Chain B consists of 30 amino acid residues.


The total number of amino acid units is \(21 + 30 = 51\).
Quick Tip: Insulin structure: Chain A (21) + Chain B (30) = 51 amino acids. It was the first protein to have its sequence determined (by Frederick Sanger).