Using one-group theory, derive the expressions for flux and the conditions for criticality for the following reactors : 

a. An infinite slab reactor of thickness a surrounded by infinitely thick reflectors on both sides. 

b. An infinite slab reactor of thickness a (cm) surrounded by thickness b (cm) reflectors on both sides. 

Please use the following notations for diffusion coefficients and macroscopic absorption and fission cross sections (also for a)): 

Core : D_c,∑_ac,v∑_fc

Reflector : D_r,∑_ar

c. For the infinite slab reactor surrounded by infinitely thick reflectors on both sides, determine the critical thickness of the core with the following data :

D_c=9.21cm, v∑_fc=0.157cm^-1, ∑_ac=0.150cm^-1

D_r=290.0cm, ∑_ar=0.004cm^-1

d. What is the critical size for the reactor given in (c) without reflector ?