(a) Calculate the ratio of probability of finding the 1s electron of hydrogen atom at r = a₀ and at r = 10a₀, where 'r' is the distance from the nucleus and a₀ = radius of the first Bohr orbit. (5 marks)

(b) Construct the Born-Haber cycle for the fo

Question

(a) Calculate the ratio of probability of finding the 1s electron of hydrogen atom at r = a₀ and at r = 10a₀, where 'r' is the distance from the nucleus and a₀ = radius of the first Bohr orbit. (5 marks)

(b) Construct the Born-Haber cycle for the formation of sodium chloride crystal at 298 K from the elements in their normal states of existence. Mention the names of the involving processes. Indicate which of them are energy demanding and which are energy evolving. (5 marks)

(c) Germanium and Silicon elements have very low electrical conductivity. How can the electrical conductivity be enhanced by adding other elements in trace amount? Explain by examples. (5 marks)

(d) Two sheets of copper of area 1·50 m² are separated by 10 cm. What is the rate of transfer of heat by conduction from the warm sheet (50°C) to the cold sheet (−10°C)? What is the rate of loss of heat? (Assume the space between the two sheets is filled with air)
Given: Coefficient of thermal conductivity of air = 2·4 × 10⁻² Js⁻¹ m⁻¹ K⁻¹ (5 marks)

(e) Why do liquids become superheated before boiling? Explain using Kelvin equation. (5 marks)

(f) Arrange the following molecules in the ascending order of their dipole moment values. Justify your answer.
NH₃, NF₃ and H₂O (5 marks)

(g) 0·500 g of benzoic acid was burnt under oxygen. The combustion produced a temperature rise of 1·236 K. The same calorimetric set-up was used to burn 0·300 g of naphthalene and the resulting temperature rise was 1·128 K. The heat of combustion of benzoic acid, ΔcU²⁹⁸ = – 3227 kJ mol⁻¹. What is the heat of combustion of naphthalene? (5 marks)

(h) A sealed container contains a gaseous sample at 300 K consisting of either pure ethane, or pure neon, or a mixture of the two. The pressure inside the container at this temperature is 1·00 atm. When the container is cooled to 150 K, the pressure is 0·37 atm. What is the composition of the sample; pure ethane, pure neon or a mixture of both? Explain your answer.
Given: Vapour pressure of C₂H₆ at 150 K is 0·10 atm
Critical temperature of neon = 44 K (5 marks)

(i) The surface area of an object to be gold plated is 49.8 cm², and the density of gold is 19.3 g/cm³. A current of 3.25 A is applied to a solution that contains gold in the +3 oxidation state. Calculate the time required to deposit an even layer of gold, 1 × 10⁻³ cm thick, on the object.
(Given: Molecular mass of gold = 196.97 g/mol) (5 marks)

(j) A steam turbine is operated with an intake temperature of 400°C, and an exhaust temperature of 150°C. What is the maximum amount of work the turbine can do for a given heat input 'Q'? Under what conditions is the maximum work achieved? (5 marks)

UPSC Answer Check · Accepted Answer

This multi-part question requires solving ten distinct problems spanning quantum mechanics, thermodynamics, electrochemistry, and solid-state chemistry. Allocate approximately 4-5 minutes per sub-part, prioritizing numerical accuracy and correct formula application. Begin with parts (a), (d), (g), (i), and (j) which involve direct calculations, then proceed to conceptual parts (b), (c), (e), (f), and (h). For each calculation, explicitly state the formula, substitute values with units, and present final answers with appropriate significant figures. - Part (a): Apply radial probability distribution for 1s orbital: P(r) ∝ r²e^(-2r/a₀), calculate ratio P(a₀)/P(10a₀) = (1/e²)/(100/e²⁰) = e¹⁸/100 - Part (b): Construct complete Born-Haber cycle for NaCl showing: sublimation of Na (endothermic), ionization of Na (endothermic), dissociation of Cl₂ (endothermic), electron gain by Cl (exothermic), lattice formation (exothermic) - Part (c): Explain doping in semiconductors—n-type (adding P/As to Si/Ge) and p-type (adding B/Ga to Si/Ge) with band theory and increased conductivity mechanism - Part (d): Apply Fourier's law of heat conduction: dQ/dt = kA(ΔT/d), calculate heat transfer rate using given thermal conductivity of air - Part (e): Explain superheating using Kelvin equation ln(p/p₀) = 2γVₘ/rRT, showing how small bubble radius creates high vapor pressure barrier delaying boiling - Part (f): Compare dipole moments considering lone pair contributions and bond polarity: NF₃ (0.23 D) < NH₃ (1.47 D) < H₂O (1.85 D), explain opposing effects in NF₃ - Part (g): Use calorimetry principle—determine calorimeter constant using benzoic acid data, then calculate naphthalene heat of combustion from temperature rise - Part (h): Apply ideal gas law and concept of condensation; neon remains gas at 150 K (T >> Tc), ethane partially condenses (P < vapor pressure), so mixture shows intermediate pressure behavior - Part (i): Apply Faraday's laws: calculate mass of Au from volume and density, use m = ZIt where Z = M/nF, determine time for electrodeposition - Part (j): Calculate Carnot efficiency η = 1 - T₂/T₁ for maximum work, state conditions: reversible operation, infinite time, no entropy generation

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Demonstrates flawless understanding across all ten parts: correct radial probability interpretation in (a), accurate Born-Haber cycle energy classification in (b), precise band theory explanation for doping in (c), proper superheating phenomenon explanation using Kelvin equation in (e), correct molecular geometry and lone pair analysis for dipole moments in (f), and accurate phase behavior interpretation in (h)	Shows basic understanding of most concepts but with minor errors: misidentifies some energy terms in Born-Haber cycle, incomplete explanation of n-type vs p-type doping, or superficial treatment of Kelvin equation application	Fundamental conceptual errors: confuses probability density with radial probability in (a), incorrectly classifies energy changes in (b), fails to distinguish doping types in (c), or completely misapplies thermodynamic principles in (h)
Mechanism / equation	20%	10	States all relevant equations correctly with proper symbols: radial probability P(r) = 4πr²\|ψ\|², Kelvin equation, Fourier's law, Carnot efficiency, Faraday's laws, ideal gas law, and calorimetry relations; explains physical significance of each term	Writes most equations correctly but with minor notational errors or missing terms; can apply equations but shows limited understanding of their derivation or conditions of validity	Incorrect or missing equations; confuses similar-looking formulas (e.g., uses probability density instead of radial probability); applies equations in inappropriate contexts without checking validity conditions
Numerical accuracy	25%	12.5	All calculations precise with correct unit handling: ratio in (a) ≈ 6.6 × 10⁶, heat transfer in (d) ≈ 21.6 W, naphthalene ΔcU ≈ -5150 kJ/mol in (g), plating time in (i) ≈ 123 s, maximum efficiency in (j) ≈ 0.388 or 38.8%	Correct methodology but arithmetic errors or unit conversion mistakes; answers in correct order of magnitude but imprecise; inconsistent significant figure usage	Major calculation errors, wrong formulas applied numerically, incorrect unit conversions (e.g., cm to m errors in d and i), or answers without any numerical working shown
Diagram / structure	15%	7.5	Clear Born-Haber cycle diagram in (b) with all five processes labeled, arrows indicating direction and energy flow; well-structured presentation of all ten answers with proper labeling and organization	Basic Born-Haber cycle present but missing some labels or energy flow indicators; answers organized but lacking visual clarity; some parts without proper structural presentation	Missing or incorrect diagram for (b); disorganized answer structure; no visual representation where required; illegible or confusing presentation of multi-part answers
Application context	20%	10	Connects theory to practical relevance: semiconductor doping for India's electronics industry (c), thermal insulation applications in building design (d), electrochemical plating in jewelry/technology (i), steam turbine efficiency in power plants (j), and calorimetry in fuel analysis; uses appropriate Indian context where relevant	Brief mention of practical applications without elaboration; standard examples without specific context; understands relevance but does not articulate connections clearly	No practical context provided; purely theoretical treatment; fails to recognize real-world significance of any calculated quantity or explained phenomenon

Q1

Directive word: Solve

How this answer will be evaluated

Approach

Key points expected

Evaluation rubric

Practice this exact question

More from Chemistry 2025 Paper I