- #1
Incand
- 334
- 47
Homework Statement
Naturally occurring uranium contains 0.7% ##\;^{235}U## and 99.3% ##\; ^{238}U## . To enrich it one uses a method based on repeated effusion.
a) Consider a step in this process. In a container, which is divided in two parts by a porous plug, one part contains natural uranium in the form of uranium hexaflouride ##UF_6## (gaseous). And the second part vacuum. Calculate the concentration of ##\;^{235}U## in this part when the system through continuous filling and pumping reach equilibrium.
b) How many times must the effusion process be repeated to get 20% ##\;^{235}U##
Homework Equations
Number of collisions per second and area (where m is the mass of an individual particle)
##v^* = \frac{1}{4}n\langle v \rangle = \frac{p}{\sqrt{2\pi mkT}}##
The Attempt at a Solution
I'm assuming the form of the uranium (##UF_6##) is irrelevant and we can simply use the 99.3% and 0.7% concentrations (of mass I assume).
Assuming natural uranium enters the chamber at the same rate that the current concentration of mass leaves we have ##m_{in} = m_{out}##.
##m_{238} = \frac{M}{N_A} = \frac{238}{6.02\cdot 10^{23}}##
##m_{235} = \frac{M}{N_A} = \frac{235}{6.02\cdot 10^{23}}##
I got ##m_{in} = m_{out} = (m_{238out} + m_{235out}) \propto (v^*_1 + v^*_2)##. At this point I'm stuck. I don't know anything about the pressure or temperature or how many of the collisions get through the plug. Any advice on how to continue?
Last edited: