I - EXERCISES:

Questions-

1. Identify the constituent parts and describe the basic structure of an atom.

2. Define the following terms: isotope, half-life, and mean free path.

3. Define fissile, fissionable, and fertile. Identify the major nuclides in each of these three categories.

4. Describe the distribution of energy among the product particles and radiations associated with fission. Explain the basis for decay heat.

5. Sketch the relationship among the following reactor cross sections:

a. total interaction

b. scattering

c. absorption

d. fission

e. capture

6. Differentiate between microscopic and macroscopic cross sections.

Numerical Problems-

7. Consider a thermal-neutron fission reaction in ²³⁵U that produces two neutrons.

a. Write balanced reaction equations for the two fission events corresponding to the fragments in Fig. 2-7.

b. Using the binding-energy-per-nucleon curve (Fig. 2-1), estimate the total binding energy for 235U and each of the fragments considered in (a).

c. Estimate the energy released by each of the two fissions and compare the results to the accepted average value.

8. The best candidate for controlled nuclear fusion is the reaction between deuterium and tritium. The reaction is also used to produce high energy neutrons.

a. Write the reaction equation for this D-T reaction.

b. Using nuclear mass values in Table 2-4, calculate the energy release for the reaction.

c. Calculate the reaction rate required to produce a power of I W, based on the result in (b).

d. Compare the D-T energy release to that for fission on per-reaction and per-reactant-mass bases.

9. Gamma rays interacting with ⁹₄Be or ²₁H produce "photoneutrorts." Write the reaction equation for each and calculate the threshold gamma energy.

10. The nuclide ²¹⁸₈₄Po emits either an alpha particle or a beta particle with a half-life of 3.10 min.

a. Write equations for each reaction.

b. Calculate the decay constant A and mean lifetime r.

c. Determine the number of atoms in a sample that has an activity of 100 μCi.

d. Calculate the activity after I, 2, and 2.5 half-lives.

II - Reactor Engineering Homework:

1. Calculate how many fuel bundles are needed for a Boiling Water Reactor (BWR) core for 2 years fuel cycle.

• Assume that 1/4 of the bundles in the core have the enrichment of feed enrichment and rest is average core enrichment (_~3 w/o U-35).
• Assume that feed enriched bundles produce 3/2 times more power than average enriched bundles.
• The BWR conditions are given below:

2. What is the surface fuel-centerline temperature depending on axial dimension (x) in a PWR core (whose specifications are given below) when the following parameters are updated ONLY?

• Thermal power decreased to 300MW
• Normalized linear heat generation rate is given as

q' (x)/q'_max = sin (x/L * 2.5)

• where x and L are in meters unit.
• Core outlet temperature will be different than the value given in the table below
• When you find fuel-centerline temperature, fuel-centerline temperature will depend on JUST x and inlet coolant temperature, nothing else (Surface temperature, etc...), at your final equation

3. What are the 3 energy group neutron diffusion equations and boundary conditions for the 3 regions of the following reactor core design?

• Radius of Small Sphere (in meter): r₁ based on spherical coordinate
• Radius of Big Sphere (in meter): r₂ based on spherical coordinate
• Small Sphere is made of UC particles
• Big box (excluding small box) is made of just graphite
• The centers of both big and small spheres are aligned to (0,0,0) coordinate point.
• Outside of big sphere is infinite medium which is filled with Inert gas (He) gas.
• Consider both down and up-scattering in 3 energy groups.

4. The reactivity in a steady state thermal reactor, in which the neutron lifetime is 0.001s, is suddenly made 0.0011positive; assuming one group of delayed neutrons, determine the subsequent change of neutron flux with time?

5. The point kinetic equations depending on time (t) are given below:

dn/dt = k(ρ - β) n/l + _i=1Σ⁶λ_iC_i.

dCi/dt = β_ik_∞ΣaΦ - λ_iC_i.

• Reactivity depends on fuel temperature (T):

o ρ(T) = (1-1/T)/100        (between 280F and 310F fuel)

• There is also a step reactivity insertion:

o ρ = 0.001          (when time ≥ 0 seconds )

• The reactor is critical at t=0

What is "s" dependent solution of point kinetic equations?

6. Describe the Emergency Core Coolant Systems of the following reactors:

1. HTGR

2. NuScale SMR

3. BWR

7. Write the radioactive equilibrium equations for Po214 considering all the atoms given in U-28 Decay series diagram below.

Hint: You can give use your own notation for the decay constant for each atom. For instance, the decay constant from U38 to Th234 is λ_U38.