# NE STUD 124 Study Guide - Midterm Guide: Plutonium-239, Light-Water Reactor, Depleted Uranium

NE124 Radioactive Waste Management, Fall 2006

Department of Nuclear Engineering, University of California, Berkeley

141 © 1995-2006 Joonhong Ahn

University of California

Department of nuclear Engineering

NE 124

Mid-Term Examination I

Fall 2006

Professor J. Ahn

CLOSED BOOK

12:40 pm – 2:00 pm, October 5, 2006

(Undergraduate students: choose any 4 problems, and answer.

Graduate students: answer all 5 problems.)

1. (15 points) Consider transmutation of plutonium 239 by a light water reactor. We assume that fresh

fuel initially contains N28

o atoms of U-238 and N49

o atoms of Pu-239. To simplify, we assume that the fresh

fuel contains no U-235. We also neglect the production of Pu-239 in the core by absorption of resonance

neutrons in U-238. Plutonium 239, therefore, is generated only by thermal neutron capture by U-238 and

consumed by its fission. Assume that the thermal flux φM is constant with time and uniform in the core. The

number, N28

o, of U-238 atoms is assumed to be constant with time. The absorption cross section of Pu-239

is σ49. The absorption cross section of U-238 is σ28. t is time.

(a) (5 points) Write the governing equation and the initial condition for the number, N49(t), of Pu-239 atoms

in the reactor core. Solve the equation.

(b) (5 points) Define and formulate the burn-up for this system in terms of the parameters in this model.

(c) (5 points) To avoid breeding of 239Pu in the fuel (i.e., to keep the number of atoms of 239Pu always

smaller than N49

o), what condition need to be satisfied among the parameters in this model?

2. (15 points) The figure below shows the current fuel flow in the United States. It shows that 201 metric

ton of natural uranium is necessary to operate 1000MWe power reactor for one calendar year. In the figure,

the capacity factor=0.8 and the heat-to-electricity conversion efficiency =0.325 are assumed. Calculate the

natural uranium requirement for 1 GWe electricity generation for one calendar year for the following cases:

(a) (5 points) The concentration of 235U in the depleted uranium is reduced to 0.2%.

(b) (5 points) The capacity factor is increased to 0.95.

(c) (5 points) The heat-to-electricity conversion efficiency is increased to 0.34.