MPHE-027 Solved Assignment January 2026 | NANOSCIENCE | IGNOU MSCPH

Q1. Attempt the following sub-questions.

Key Points:

Top-down synthesis reduces bulk materials into nanoparticles.
Ball milling uses mechanical force; it's scalable but can cause contamination and broad size distribution.
Lithography (e.g., EBL) patterns materials precisely; it's high-resolution but costly and slow.
HRTEM transmits electrons through a thin sample to image atomic structures.

Answer: Nanoscience often employs 'top-down' synthesis approaches, which involve reducing larger bulk materials into nano-sized structures. These methods typically start with macroscopic objects and use various techniques like mechanical force or patterning to achieve nanometer dimensions. Two common examples are ball milling and lithography, each with distinct principles and applications. Ball milling is a mechanical attrition method where larger materials are subjected to high-energy collisions from ...

Q1(a). For an icosahedral cluster calculate the number of atoms present in its 7th shell. Find the total number of atoms in this cluster and its surface to bulk atom ratio.

(a)) For an icosahedral cluster calculate the number of atoms present in its 7th shell. Find the total number of atoms in this cluster and its surface to bulk atom ratio. (200 words)

Key Points:

Icosahedral clusters have specific 'magic numbers' of atoms.
Atoms in the k-th shell: `N_k = 10k² + 2` (k=shell number).
Total atoms in a k-shell cluster: `N_total(k) = (10k³ + 15k² + 11k + 3) / 3`.
Surface atoms are those in the outermost shell.

Answer: Icosahedral clusters are common magic number clusters in nanoscience, characterized by a central atom surrounded by successive shells of atoms. The calculation of atoms in specific shells, total atoms, and surface-to-bulk ratio is crucial for understanding their properties, which often differ significantly from bulk materials due to high surface area.

Q1(b). Draw the LaMer diagram and explain the particle growth in its three regions.

Key Points:

LaMer diagram plots monomer concentration versus time during nanoparticle synthesis.
C_crit is the critical concentration required for new particle nucleation.
C_sat is the equilibrium saturation concentration for monomer growth on existing particles.
Region I: Monomer concentration increases below C_crit, building supersaturation.

Answer: The LaMer diagram is a fundamental conceptual model depicting the time-evolution of monomer concentration during nanoparticle synthesis, essential for controlling particle size distribution. It typically plots the concentration of the monomer (y-axis) against time (x-axis), illustrating two critical thresholds: the critical nucleation concentration (C_crit) and the saturation concentration (C_sat). Region I represents the initial phase where the precursor monomer concentration steadily increase...

Q2. Attempt the following sub-questions.

Key Points:

The specific question for the MPHE-027 Nanoscience course is currently missing from the prompt.
A comprehensive answer requires the exact question to extract relevant content and examples.
Answers would be structured in short paragraphs (3-4 sentences) with `\n\n` separators.
Calculations would be step-by-step in plain text with appropriate Unicode symbols.

Answer: I apologize, but the specific question you want me to answer for the MPHE-027 Nanoscience course is missing from your prompt. To provide a comprehensive and accurate response, extracting specific content, examples, formulas, and explanations from the course PDF, the question itself is essential. If the question were provided, I would analyze its scope (e.g., whether it concerns quantum mechanical effects, synthesis methods, characterization techniques, or applications of nanomaterials) to ensur...

Q2(a). Describe the set up used for ionized cluster beam (ICB) deposition. What are the advantages of this method?

Key Points:

ICB setup involves source vaporization, cluster formation via adiabatic expansion.
Neutral clusters are partially ionized by electron impact, then electrostatically accelerated.
Both ionized and neutral clusters deposit on the substrate in high vacuum.
Enhanced film adhesion due to high kinetic energy of impacting clusters.

Answer: The Ionized Cluster Beam (ICB) deposition setup begins with an evaporation crucible containing the source material, which is heated to generate vapor. This vapor expands adiabatically through a small nozzle into a high vacuum chamber, leading to homogeneous nucleation and the formation of atomic or molecular clusters, typically containing 100 to 1000 atoms. Subsequently, these neutral clusters pass through an electron impact ionizer, where a fraction of them acquire a positive charge. The ioniz...

Q2(b). Explain the steps of sol-gel synthesis of silica gel. Differentiate between the structure and method of formation of xerogel and aerogel.

Key Points:

Sol-gel synthesis starts with alkoxide hydrolysis to form silanol groups.
Condensation reactions form siloxane bonds, leading to a 3D gel network.
Xerogels are dense, low porosity materials formed by evaporative drying.
Aerogels are highly porous, low-density materials formed by supercritical drying.

Answer: Sol-gel synthesis of silica gel involves a series of chemical reactions, primarily hydrolysis and condensation, starting from a molecular precursor. First, **hydrolysis** occurs when an alkoxide precursor, such as tetraethyl orthosilicate (TEOS), reacts with water, often catalyzed by acid or base. This reaction replaces the alkoxy (–OR) groups with hydroxyl (–OH) groups, forming silanol groups (Si–OH). An example reaction is Si(OR)₄ + nH₂O → Si(OH)n(OR)₄-n + nROH. Next, **condensation** reacti...

Q2(c). What is meant by bio-template? With an example explain how it can be used in nanostructure synthesis. State the advantages of using green methods for nanomaterial synthesis.

Key Points:

Bio-template: Biological entity (virus, DNA) as scaffold for nanostructure synthesis.
Offers precise control over nanostructure shape, size, and orientation.
Example: Tobacco Mosaic Virus (TMV) templates for nanowire fabrication.
TMV's uniform dimensions allow controlled growth of 1D nanostructures.

Answer: A bio-template refers to a biological entity, such as viruses, bacteria, DNA, proteins, or plant structures, that serves as a pre-formed scaffold or mold for the directed synthesis of inorganic nanostructures. These biological templates possess inherent structural organization, enabling precise control over the shape, size, and orientation of the fabricated nanomaterials. For example, the Tobacco Mosaic Virus (TMV) can act as an effective bio-template. Its rod-like shape and uniform dimensions ...

Q3. Attempt the following sub-questions.

Key Points:

Quantum confinement restricts charge carrier movement in materials 1-100 nm in size.
Occurs when material dimensions are comparable to the de Broglie wavelength of carriers.
Leads to quantized, discrete energy levels, replacing continuous energy bands.
Increases the effective band gap of semiconductor nanomaterials as size decreases (blue shift).

Answer: Quantum confinement is a fundamental phenomenon in nanoscience, occurring when the dimensions of a material become comparable to or smaller than the de Broglie wavelength (λ = h/p) of its charge carriers, typically in the 1-100 nm range. This spatial restriction limits the movement of electrons and holes in one, two, or three dimensions. As discussed in MPHE-027, Unit 1, this confinement dramatically alters the material's intrinsic electronic and optical properties compared to its bulk counterpa...

Q3(a). Explain the structure and bonding pattern in C60 Fullerene. Which nanocrystalline allotropes of carbon are obtained using the electric arc deposition set-up with graphite rods?

Key Points:

C60 fullerene is a truncated icosahedron, resembling a soccer ball structure.
It consists of 60 sp² hybridized carbon atoms arranged in 12 pentagons and 20 hexagons.
Each carbon atom in C60 is bonded to three others, with two distinct C-C bond lengths.
C60 features delocalized π electrons, imparting stability and aromatic characteristics.

Answer: C60 fullerene, also known as Buckminsterfullerene, possesses a unique closed-cage structure resembling a soccer ball or a truncated icosahedron. It consists of 60 carbon atoms arranged in 12 pentagonal and 20 hexagonal rings. Each carbon atom in C60 is sp² hybridized, contributing to its robust yet flexible spherical geometry. In terms of bonding, each carbon atom is covalently bonded to three other carbon atoms. The C-C bonds are not uniform; there are two distinct bond lengths. Shorter double...

Q3(b). What are Dirac point and Dirac cone in case of graphene? What are the specialties of a Dirac cone? What is the difference between graphene and graphyne?

Key Points:

Dirac point: Where graphene's conduction and valence bands meet with zero energy gap.
Dirac cone: Linear energy dispersion around Dirac points in energy-momentum space.
Massless Dirac fermions: Electrons in graphene behave as if they have zero effective mass.
Dirac cone specialties: High electron mobility and anomalous quantum Hall effect.

Answer: In graphene, the **Dirac point** refers to the specific locations in the Brillouin zone where the conduction band and valence band meet, resulting in a zero energy gap. At these points, electrons and holes behave similarly, lacking an effective mass. Around each Dirac point, the energy-momentum relationship is linear, not parabolic as in conventional semiconductors. This linear dispersion forms a conical shape in the energy-momentum diagram, known as the **Dirac cone**. This unique electronic s...

Q4. Attempt the following sub-questions.

Key Points:

Quantum confinement makes energy levels discrete, increasing bandgap in nanomaterials.
Quantum dots' emission color is size-tunable due to quantum confinement effect.
Top-down synthesis (e.g., Ball Milling) reduces bulk material to nanoscale.
Bottom-up synthesis (e.g., Sol-Gel) builds nanomaterials from atomic precursors.

Answer: This response addresses three common sub-questions in Nanoscience, drawing upon typical content found in courses like MPHE-027. We will explain quantum confinement, describe two synthesis methods, and discuss two applications of nanotechnology. ### Sub-question 1: Explain the concept of quantum confinement and its effect on the properties of nanomaterials, particularly quantum dots. Quantum confinement is a phenomenon that occurs when the dimensions of a material are reduced to the nanoscale, ...

Q4(a). Explain with examples, what are Janus particles. Which synthesis methods can be used to form such particles?

Key Points:

Janus particles are anisotropic nanoparticles with two distinct physical/chemical properties.
Named after the two-faced Roman god, enabling unique directional interactions.
Example: One hemisphere hydrophilic, the other hydrophobic for nanoscale surfactants.
Synthesis method 1: Partial surface modification using templates or interfaces.

Answer: Janus particles are a fascinating class of anisotropic nanoparticles, named after the two-faced Roman god, characterized by having two or more distinct physical or chemical properties segregated on their surface. This inherent asymmetry allows them to exhibit unique directional interactions and functionalities, unlike their isotropic counterparts. For instance, a classic example of a Janus particle would be one with a hydrophilic hemisphere and a hydrophobic hemisphere. Another common example i...

Q4(b). Calculate the surface plasmon energy of a metal with free electron density of 8×1027 m-3.

Key Points:

Surface plasmon energy is derived from the bulk plasma frequency.
Bulk plasma frequency (ω_p) formula: √(ne² / (m_eε₀)).
ω_p depends directly on the free electron density (n).
Surface plasmon frequency (ω_sp) is ω_p / √2 for metal-air interface.

Answer: The surface plasmon energy (E_sp) is derived from the metal's bulk plasma frequency (ω_p), which depends on the free electron density (n). The formula for bulk plasma frequency is ω_p = √(ne² / (m_eε₀)), where e is elementary charge, m_e is electron mass, and ε₀ is permittivity of free space. Given n = 8 × 10²⁷ m⁻³, the bulk plasma frequency is calculated as: ω_p = √((8×10²⁷ × (1.602×10⁻¹⁹)² ) / (9.109×10⁻³¹ × 8.854×10⁻¹²)) ω_p ≈ 5.044 × 10¹⁵ rad/s. For a metal-air interface, the surface plasm...

Q4(c). What are surface plasmon polaritons (SPP)? State any two technological applications of SPP.

Key Points:

SPPs are collective electron oscillations at metal-dielectric interfaces.
They are electromagnetic waves coupled to these surface electron oscillations.
SPPs propagate along the interface and decay evanescently into media.
A key feature is the strong local electromagnetic field enhancement.

Answer: Surface Plasmon Polaritons (SPP) are coherent, collective oscillations of free electrons at the interface between a metal (typically with a negative real part of permittivity) and a dielectric medium. These electron oscillations are coupled with electromagnetic waves, forming a unique type of quasi-particle that propagates along the interface. SPPs are confined to the surface and exhibit evanescent decay into both the metal and dielectric, leading to significant enhancement of the local electro...

Q4(d). What is exciton? What is the difference between Frenkel and Mott-Wannier excitons? Calculate the radius of an exciton in a semiconductor with dielectric constant ε = 9.1, me = 0.2 and mp = 0.55.

Key Points:

An exciton is a neutral quasiparticle: a bound electron-hole pair.
Excitons transport energy without net charge, formed by photon excitation.
Frenkel excitons are tightly bound, small radius, localized, high binding energy.
Mott-Wannier excitons are loosely bound, large radius, extended, low binding energy.

Answer: An exciton is an electrically neutral quasiparticle, a bound state of an electron and an electron hole in semiconductors or insulators. It forms when light excites an electron from the valence band to the conduction band, leaving a positively charged hole. This electron-hole pair is attracted by Coulomb force, allowing it to transport energy without carrying net electric charge within the material. Excitons are categorized into two main types: Frenkel and Mott-Wannier excitons. Frenkel excitons...

Q5. Attempt the following sub-questions.

Key Points:

Nanoscience deals with materials at 1-100 nm, showing unique properties.
Increased surface area to volume ratio enhances material reactivity.
Quantum confinement leads to discrete energy levels in nanomaterials.
Quantum dots exhibit size-dependent light emission due to confinement.

Answer: Nanoscience explores phenomena and manipulation of materials at the nanoscale, typically between 1 to 100 nanometers. At this dimension, materials exhibit unique properties drastically different from their bulk counterparts, primarily due to the increased surface area to volume ratio and quantum mechanical effects. One fundamental principle is the **increased surface area to volume ratio**. As the size of a material decreases, its surface atoms become a significantly larger proportion of the to...

Q5(a). Explain the difference between ballistic transport and normal (diffusive) transport in a material. Using the Landauer formula, calculate the conductance of a quantum device in which the conduction take place through three channels, each of which has a transmission coefficient T=1.

Key Points:

Ballistic transport: Electrons travel without scattering (MFP > device length).
Diffusive transport: Electrons scatter frequently (MFP < device length).
Landauer formula: G = (2e²/h) * Σ T_n, for quantum conductance.
Quantum of conductance (G₀) is 2e²/h, approximately 7.748 × 10⁻⁵ S.

Answer: In nanoscience, electron transport in materials is categorized primarily into ballistic and diffusive regimes, depending on the length scale and scattering events. **Ballistic Transport** Ballistic transport occurs when electrons travel through a material or device without undergoing any scattering events, such as collisions with phonons, impurities, or defects. In this regime, the mean free path (MFP) of the electron is significantly larger than the length of the conductor. This typically happ...

Q5(b). Derive the expression for the conductivity matrix in integer quantum Hall effect.

Key Points:

IQHE conductivity matrix describes transport in strong B-fields, low T, and 2D systems.
In IQHE, longitudinal conductivity (σ_xx) vanishes due to electron localization.
Hall conductivity (σ_xy) arises from E×B drift velocity of charge carriers.
Classical drift gives σ_xy = n_s e / B and σ_yx = -n_s e / B.

Answer: The Integer Quantum Hall Effect (IQHE) describes the precise quantization of Hall conductivity in two-dimensional electron systems at low temperatures and strong magnetic fields. The conductivity matrix (or tensor) relates the current density (J) to the applied electric field (E) and is crucial for understanding charge transport in this regime. To derive the conductivity matrix, we start with the classical motion of electrons in crossed electric (E) and magnetic (B) fields. In the ideal IQHE pl...

Q6. Attempt the following sub-questions.

Key Points:

Nanomaterials (1-100 nm) exhibit properties distinct from bulk materials due to quantum confinement and increased surface area-to-volume ratio.
Quantum confinement leads to quantized energy levels, enabling size-tunable emission colors in semiconductor quantum dots.
Surface Plasmon Resonance (SPR) causes gold nanoparticle colors to vary with size, due to collective electron oscillations.
Carbon nanotubes' electrical properties (metallic or semiconducting) depend on their diameter and chirality, a nanoscale quantum effect.

Answer: Nanomaterials, typically defined as materials with at least one dimension in the range of 1 to 100 nanometers, exhibit properties fundamentally different from their bulk counterparts. These alterations arise primarily from two key phenomena: quantum confinement effects and the dramatically increased surface area-to-volume ratio. Quantum confinement occurs when the material's dimensions become comparable to or smaller than the de Broglie wavelength of its electrons or excitons. This confines the...

Q6(a). What is the difference between single domain and superparamagnetic particles? A superparamagnetic material has a characteristic time of 10-11 seconds and a Néel relaxation time of 2.0 second at 300 K. Calculate i) the energy barrier (in eV); and ii) the blocking temperature if the measurement time is 120s. Take kB = 8.62 × 10-5 eVK-1.

Key Points:

Single domain particles contain one magnetic domain with stable magnetization.
Superparamagnetic particles are single domain but show thermally driven magnetization flips.
The difference is thermal energy overcoming anisotropy barrier, relative to measurement time.
Néel relaxation time describes the characteristic time for magnetization flipping.

Answer: Single domain particles are magnetic nanoparticles that are small enough to consist of only one continuously magnetized region, meaning all atomic magnetic moments within the particle are aligned in a single direction. They exhibit stable magnetization, acting as tiny, permanent magnets below a certain temperature. Superparamagnetic particles are a specific type of single-domain particle where the thermal energy (k_B T) is comparable to or greater than the magnetic anisotropy energy barrier (E_...

Q6(b). What are single negative and double negative materials? Explain with the help of a diagram, the characteristics of the propagation of electromagnetic waves through a double negative material.

Key Points:

Single negative materials have either ε < 0 or μ < 0, but not both.
Double negative materials (DNGs) possess both ε < 0 and μ < 0 simultaneously.
DNGs are also called Left-Handed Materials (LHMs) or Veselago materials.
EM waves in DNGs exhibit a negative refractive index (n < 0).

Answer: Single negative (SNG) materials are a class of exotic materials where either the electric permittivity (ε) is negative (ε < 0) or the magnetic permeability (μ) is negative (μ < 0), but not both simultaneously. An example of an epsilon-negative (ENG) material is plasma below its plasma frequency, while mu-negative (MNG) materials can be realized using certain resonant structures. Double negative (DNG) materials, also known as Left-Handed Materials (LHMs) or Veselago materials, are those where bo...

Q6(c). Describe the property of band inversion in a topological insulator. Hence explain why a topological insulator cannot be transformed into a normal insulator.

Key Points:

Band inversion: Reversal of conduction and valence band order at specific Brillouin zone points.
Driven by strong spin-orbit coupling (SOC) in topological insulators.
Topological insulators have an 'inverted' bulk band structure.
Characterized by a non-trivial topological invariant (e.g., Z₂ invariant).

Answer: Band inversion is a defining characteristic of topological insulators (TIs), where the conventional energetic order of the conduction and valence bands at certain high-symmetry points in the Brillouin zone reverses. This phenomenon is primarily driven by strong spin-orbit coupling (SOC), which causes the band structure to invert. For instance, while a normal insulator (NI) has a standard band ordering, a TI exhibits an 'inverted' bulk band structure. This inversion leads to distinct electronic...

Q7. Attempt the following sub-questions.

Key Points:

Nanomaterials (1-100 nm) exhibit unique properties differing from bulk materials.
High surface-area-to-volume ratio enhances reactivity for catalysis and sensing.
Quantum confinement effect leads to size-dependent optical and electrical properties.
Quantum dots change emission color based on size, useful for displays and imaging.

Answer: Nanomaterials are defined as materials with at least one dimension in the range of 1 to 100 nanometers (nm). At this scale, materials often exhibit properties significantly different from their bulk counterparts, primarily due to an increased surface-area-to-volume ratio and quantum mechanical effects. These unique properties form the foundation for numerous applications in various fields. One of the most prominent unique properties is the exceptionally high surface-area-to-volume ratio. As par...

Q7(a). Explain the construction and working principle of a microfluidic cantilever sensor. What is the resolution attained by such sensor?

Key Points:

Microfluidic cantilever: MEMS-fabricated beam with integrated microfluidic channel.
Construction: Cantilever functionalized with receptor layer for specific analyte binding.
Working principle: Analyte binding induces differential surface stress, causing cantilever deflection.
Detection methods: Deflection measured optically (laser) or piezoresistively.

Answer: A microfluidic cantilever sensor integrates a micro-scale beam (cantilever) with a microfluidic channel for highly sensitive detection. **Construction:** The sensor typically comprises a miniature, beam-like cantilever fabricated using Micro-Electro-Mechanical Systems (MEMS) technology, often from silicon or silicon nitride. One side of the cantilever is functionalized with a specific receptor layer designed to selectively bind the target analyte. A microfluidic channel is precisely integrated ...

Q7(b). Describe the detection mechanism of a virus with the use of Up-Conversion Nanoparticles (UCNPs).

Key Points:

UCNPs convert low-energy NIR light to high-energy visible/UV emission.
Lanthanide-doped UCNPs reduce biological autofluorescence noise.
UCNPs are functionalized with antibodies/aptamers for specific viral binding.
Detection often employs a sandwich immunoassay format.

Answer: Up-Conversion Nanoparticles (UCNPs) offer a highly sensitive and selective platform for virus detection, leveraging their unique optical properties. These nanoparticles are typically lanthanide-doped (e.g., Yb³⁺, Er³⁺) and possess the ability to convert low-energy Near-Infrared (NIR) light into higher-energy visible or ultraviolet emission. This upconversion process is advantageous because biological samples exhibit minimal autofluorescence in the NIR region, leading to a high signal-to-noise r...

Q8. Attempt the following sub-questions.

Key Points:

Quantum confinement discretizes energy levels when material dimensions are reduced to nanoscale.
Quantum wells confine carriers in one dimension, quantum wires in two, quantum dots in three.
Confinement widens the effective band gap and shifts optical absorption/emission to higher energies (blue shift).
Density of states transforms from continuous to staircase-like (2D), sharp peaks (1D), or discrete (0D).

Answer: Quantum confinement is a fundamental phenomenon observed when the dimensions of a material are reduced to the nanoscale, comparable to or smaller than the exciton Bohr radius of the bulk material. This spatial restriction of electrons, holes, or excitons leads to the discretization of energy levels that were continuous in the bulk material. Consequently, the electronic and optical properties of these nanomaterials deviate significantly from their bulk counterparts. This confinement effect arise...

Q8(a). What are triboelectric nanogenerators? Explain the different modes of their operation.

Key Points:

TENGs convert mechanical energy into electrical energy using triboelectric effect and electrostatic induction.
Triboelectric effect involves charge transfer between materials upon contact, creating surface charges.
Vertical contact-separation mode: Materials periodically touch and separate, inducing current.
Lateral sliding mode: Surfaces slide against each other, generating charge and current.

Answer: Triboelectric Nanogenerators (TENGs) are innovative devices designed to harvest ambient mechanical energy, such as vibrations, friction, or motion, and convert it into electrical energy. Their operation relies on a synergistic coupling of the triboelectric effect (contact electrification) and electrostatic induction. Upon contact between two different materials, the triboelectric effect causes charge transfer, resulting in oppositely charged surfaces. When these charged surfaces subsequently se...

Q8(b). Describe the role of Nanotechnology in the reduction of air pollution.

Key Points:

Nanotechnology reduces air pollution via photocatalysis, adsorption, filtration, and sensing.
TiO₂ nanoparticles degrade VOCs and NOx into harmless compounds via photocatalysis under UV light.
Nanoadsorbents (CNTs, graphene) capture gaseous pollutants due to high surface area and porosity.
Nanofiber membranes efficiently filter fine particulate matter (PM2.5, PM10) with low pressure drop.

Answer: Nanotechnology plays a crucial role in reducing air pollution by leveraging the unique properties of nanomaterials, including their high surface area and enhanced reactivity. One significant application is **photocatalysis**, where nanomaterials like titanium dioxide (TiO₂) nanoparticles act as catalysts. Upon exposure to UV light, these nanoparticles generate reactive oxygen species that can oxidize and degrade harmful gaseous pollutants such as volatile organic compounds (VOCs) and nitrogen o...

Q8(c). Explain the lotus effect based on contact angle. Describe two practical applications of lotus effect.

Key Points:

Lotus effect: Superhydrophobic and self-cleaning property of certain surfaces.
Contact angle: Characterized by water contact angles typically exceeding 150°.
Mechanism: Hierarchical micro-nanoscale roughness combined with low surface energy compounds.
Wettability: Water droplets minimize solid-liquid contact by resting on trapped air pockets (Cassie-Baxter state).

Answer: The lotus effect describes the phenomenon of superhydrophobicity and self-cleaning observed on lotus leaves, which allows water droplets to roll off surfaces easily, carrying dirt particles with them. Based on contact angle, this effect is characterized by extremely high water contact angles, typically greater than 150°, and very low sliding angles (below 10°). This high contact angle indicates poor wettability, meaning the water droplet minimizes contact with the solid surface. This superhydr...

MPHE-027 Solved Assignment — January 2026 / July 2026

NANOSCIENCE | IGNOU Master of Science (Physics) Programme (MSCPH)

MPHE-027—January 2026 / July 2026

NANOSCIENCE

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MPHE-027 Assignment Questions — January 2026

Q1. Attempt the following sub-questions.

Q1(a). For an icosahedral cluster calculate the number of atoms present in its 7th shell. Find the total number of atoms in this cluster and its surface to bulk atom ratio.

Q1(b). Draw the LaMer diagram and explain the particle growth in its three regions.

Q2. Attempt the following sub-questions.

Q2(a). Describe the set up used for ionized cluster beam (ICB) deposition. What are the advantages of this method?

Q2(b). Explain the steps of sol-gel synthesis of silica gel. Differentiate between the structure and method of formation of xerogel and aerogel.

Q2(c). What is meant by bio-template? With an example explain how it can be used in nanostructure synthesis. State the advantages of using green methods for nanomaterial synthesis.

Q3. Attempt the following sub-questions.

Q3(a). Explain the structure and bonding pattern in C60 Fullerene. Which nanocrystalline allotropes of carbon are obtained using the electric arc deposition set-up with graphite rods?

Q3(b). What are Dirac point and Dirac cone in case of graphene? What are the specialties of a Dirac cone? What is the difference between graphene and graphyne?

Q4. Attempt the following sub-questions.

Q4(a). Explain with examples, what are Janus particles. Which synthesis methods can be used to form such particles?

Q4(b). Calculate the surface plasmon energy of a metal with free electron density of 8×1027 m-3.

Q4(c). What are surface plasmon polaritons (SPP)? State any two technological applications of SPP.

Q4(d). What is exciton? What is the difference between Frenkel and Mott-Wannier excitons? Calculate the radius of an exciton in a semiconductor with dielectric constant ε = 9.1, me = 0.2 and mp = 0.55.

Q5. Attempt the following sub-questions.

Q5(a). Explain the difference between ballistic transport and normal (diffusive) transport in a material. Using the Landauer formula, calculate the conductance of a quantum device in which the conduction take place through three channels, each of which has a transmission coefficient T=1.

Q5(b). Derive the expression for the conductivity matrix in integer quantum Hall effect.

Q6. Attempt the following sub-questions.

Q6(b). What are single negative and double negative materials? Explain with the help of a diagram, the characteristics of the propagation of electromagnetic waves through a double negative material.

Q6(c). Describe the property of band inversion in a topological insulator. Hence explain why a topological insulator cannot be transformed into a normal insulator.

Q7. Attempt the following sub-questions.

Q7(a). Explain the construction and working principle of a microfluidic cantilever sensor. What is the resolution attained by such sensor?

Q7(b). Describe the detection mechanism of a virus with the use of Up-Conversion Nanoparticles (UCNPs).

Q8. Attempt the following sub-questions.

Q8(a). What are triboelectric nanogenerators? Explain the different modes of their operation.

Q8(b). Describe the role of Nanotechnology in the reduction of air pollution.

Q8(c). Explain the lotus effect based on contact angle. Describe two practical applications of lotus effect.