Uranium is an element famous for its explosive and energy
providing properties. However, not all uranium atoms are equally
suited for the fission process. An atom is defined to be Uranium if
its nucleus contains 92 protons. The radioactive properties of the
uranium atom depend on the number of neutrons it possesses.
Different atoms which have the same number of protons but differing
numbers of neutrons are called isotopes. The isotope best suited
for bombs and nuclear power is the one containing 143 neutrons.
This is known as uranium-235 since it has 235 nucleons (92 protons
and 143 neutrons). Uranium which is mined from the earth contains
many different isotopes including uranium-238 (92 protons, 146
neutrons), uranium-235 (92 protons, 143 neutrons), and uranium-234
(92 protons, 142 neutrons). The process of “enriching” uranium is
one that uses mass spectrometers to separate the different isotopes
of uranium to isolate uranium-235. Because each isotope has a
different inertia (see table below), they will arc with a different
radius. (see picture below) Collectors can be set up for each
isotope to accumulate separately. However, since the inertias of
the different isotopes are very similar, this is an extremely
technical and precise process, as you shall soon see. A particular
enriching device uses a magnetic field of 0.5 T and injects singly
ionized atoms (missing one electron) into the chamber at a speed of
10 km/s. Assuming there is no variability in any of these
parameters (a REALLY big assumption!!), how far should the centers
of the collectors be separated? These distances are labeled 𝑑1 and
𝑑2 in the figure below.
Answer
