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### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# Some uranium samples from the natural reactor site described in Module 43-3 were found to be slightly enriched in ${{\mathbf{}}}^{{\mathbf{235}}}{\mathbf{U}}$, rather than depleted. Account for this in terms of neutron absorption by the abundant isotope ${{\mathbf{}}}^{{\mathbf{238}}}{\mathbf{U}}$and the subsequent beta and alpha decay of its products.

The neutron absorption by the abundant isotope of ${}^{238}\mathrm{U}$is substantially increased resulting in a faster decay rate for the beta and alpha processes.

See the step by step solution

## Step 1: Write the given data

Some uranium samples from the natural reactor site were described in Module 43-3.

## Step 2: Determine the concept of enrichment of an isotope

An isotope of a radionuclide is defined as enriched or abundant relating to various factors that occur in their beta or alpha decay processes. The availability of higher neutrons causes the fission reaction of a radionuclide resulting in their decay and thus, it causes their decay rate to be faster than others. Thus, a nuclide with faster decay is depleted by neutrons while a lower decay rate describes enrichment in the nuclide's nuclei number.

## Step 3: Calculate the neutron absorption by the uranium-238 isotope

The nuclei of ${}^{238}\mathrm{U}$can capture neutrons and beta-decay. With a large amount of neutrons available due to the fission of ${}^{235}\mathrm{U}$, the probability for this process is substantially increased, resulting in a much higher decay rate for ${}^{238}\mathrm{U}$and causing the depletion of ${}^{238}\mathrm{U}$(and relative enrichment of ${}^{235}\mathrm{U}$).

Hence, the neutron absorption by the abundant isotope of ${}^{238}\mathrm{U}$is substantially increased resulting in a faster decay rate for the beta and alpha processes.