Common types of engineering materials are metals, ceramics, polymers and composites. Compare these four classes on the basis of their composition and any two properties. State one application of each type.

State Fick's law. Discuss its importance in neutron transport /diffusion. Write the assumptions used to derive Fick's law and hence derive its expression.

Starting with the general form of transport equation, obtain the diffusion equation
$

What do you understand by constant cross-section approximation? Derive the steady state equation for a plane geometry. Also write the transport equation for a spherical geometry.

Using the transport equation for a non-multiplying system and homogeneous assembly, derive the integral form of transport equation using the method of characteristics. What do you understand by "Optical path length" of the medium?

What are (i) initial and boundary conditions, and (ii) Interface boundary conditions?

Explain the lotus effect based on contact angle. Describe two practical applications of lotus effect. 

 What are

Describe the role of Nanotechnology in the reduction of air pollution.

What are triboelectric nanogenerators? Explain the different modes of their operation.

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

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

 Derive neutron transport equation in terms of angular neutron flux for a heterogeneous multiplying assembly. Rewrite simplified form of this equation for a non-multiplying and homogeneous assembly.

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

 5 MeV neutron is scattered through an angle of 45 degrees in a collision with  nucleus. Calculate the energy of scattered neutrons and energy of the recoiling nucleus. 

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. 

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 . 

 Describe the Fermi-age theory and derive Fermi-age approximation of slowing down equation for a weak absorbing medium. Discuss the S-G approximation. 

The initial energy of a neutron is 2 MeV, calculate the maximum energy loss due to elastic scattering in . 

Show that the average cosine of scattering angle in the LAB system () is given by , where A is the mass number of nucleus. Is this relation applies to hydrogen?