Derive the expression for the conductivity matrix in integer quantum Hall effect. 

Derive the four factor formula and explain each term involves in it with mathematical steps. Hence, obtain six-factor formula. 

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 . 

Draw and explain the energy variation of fission cross-sections for  and . 

What are prompt and delayed neutrons? Discuss the role of delayed neutrons in reactor safety.

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 ,  and .

Differentiate between neutron elastic scattering and inelastic scattering. Draw elastic scattering cross-section curves for  and  and write their features. 

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

 Define reaction rate. Write its mathematical formula. Explain each term involves in it. 

 Calculate, using Weiszäcker formula, the binding energy per nucleon for .
Given: 

Calculate the surface plasmon energy of a metal with free electron density of . 

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

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?

 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?

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.

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

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

 Draw the LaMer diagram and explain the particle growth in its three regions.

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.

Discuss the role of interpersonal communication and team building in planning and implementing successful development communication initiatives.