IGNOU MPHE 26 SOLVED ASSIGNMENT

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MPHE 026 (January 2024 - July 2024) - ENGLISH

Tutor Marked Assignment

ELEMENTS OF REACTOR PHYSICS

Course Code: MPHE-026

Assignment Code: MPH-26/MA/2024-25

Max. Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.

PART A

1. a) Calculate the macroscopic scattering cross section for natural uranium. Given p-18.9 g/cm³, percentage weight of natural uraniumis 0.713; the rest being. The scattering cross sections for 2 and 2 sotopes being 15 b and 13.8b, respectively

b) Distinguish between prompt and delayed neutroninion and discus their importance.

c) The average number of neutros produced per fission is 2.5. What would happen in a second, if every neutronenfioncanother son? Assume a generation time of 0.1 second.

d) ) What is the difference between slowing down density and flux of neutron?

If the reference neutron energy is 10 Mev, calculate the lethargyat 200 kV, and 0.025 V?

* Discuss the concept of breeding and doubling time and describe how abundant fertile actinides could be converted to excellent

2. a) Define LAB and CM coordinateraofference used to study the kinematics of two-body collisionObtain an expression of kinetic energy of neutron after collision in the LA

b) A.2.6 Mev neutron collide with hydrogen Calculate the probability that the energy of neutron is within the energy range 0.63 and 0.75MeV after collisiona neutron loses 0.75MLA, what is the catering angle in the CM system?

c) Derive an expression of average logarithmic energy decrement per colon Hence, show that for large mass number, independent of energy. Using this formula, plot average logarithmic energy decrement for different nuclides of mass

d) Ifa 10 M/V neutron collided with nuclide compare the average energy loss of neuron they undergo indicating and caring

PART B

3. a) Define angular neutron flux and angular curent density. The neutron fluxata particular location in a reactor cone is 1x10 neutrona cm. What is the average density (cutrons of the thermal neutrons at the same location in the core?

b) Write the basic assumptions made to drive the transport equation. Hence, derive the Boltzmann transport equation for a multiplying system in terms of neutron flux 

c) Using spherical harmonica method for non-multiplying 1-plane geometry, write the exact infinite coupled equations. Hence for a large non-absorbing system, obtain equations under Py approximation Discuss the Imitation of P approximation.

d) Discuss the initial boundary and source condition

4. a) For an arbitrary volume of material in which one speedtronic with medium nuclei, is the neutron density and at time, obtain the equation of continuity. Also, obtain equation for steady sta

b) The scattering cross-section of Carbon at 14.8 barn. Estimate the diffusion coefficient of Carbon. Assume that is almost negligible

c) Write two-group criticality condition for a bare homogeneous reactor. Using this equation, show that the six factor criticality condition for two group theory is given by fpe 1.The symbols have their usual meanings.

d) Write the Farmi-age critical equation for a bare nector based on continuous slowing down model. Reduce to two-group critical equation for large assemblies (for small values of

MPHE 026 (January 2026 - July 2026) - ENGLISH

Tutor Marked Assignment
ELEMENTS OF REACTOR PHYSICS

Course Code: MPHE-026
Assignment Code: MPHE-026/TMA/2026
Max. Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.

---

PART A

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


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

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

d) i) What are prompt and delayed neutrons? Discuss the role of delayed neutrons in reactor safety.
ii) Draw and explain the energy variation of fission cross-sections for and . 

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

2. a) 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? 

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

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

d) 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. 

PART B

3. a) 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.

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

c) 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?

d) 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.

4. a) Starting with the general form of transport equation, obtain the diffusion equation
$

b) 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.

c) Derive two-group diffusion equations for a critical homogeneous reactor in steady state.

d) Show that the root mean square crow-flight distance for neutrons from an infinite plane source in an infinite medium is .

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