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Standard XII
Physics
First Order Radioactive Decay
Question

The uranium ore mined today contains only $$0.72 \%$$ of fissionable $$^{235}U$$,too little to make reactor fuel for thermal-neutron fission.For this reason,the mined ore must be enriched with $$^{235}U$$. Both $$^{235}U \ (T_{1/2} = 7.0 \times 10^8 \ y)$$ and $$^{238}U \ (T_{1/2} = 4.5 \times 10^9 \ y)$$ are radioactive. How far back in time would natural uranium ore have been a practical reactor fuel,with a $$^\dfrac{^{235}U}{^{238}U}$$ ratio of $$3.0 \%$$?

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Q1
The uranium ore mined today contains only $$0.72 \%$$ of fissionable $$^{235}U$$,too little to make reactor fuel for thermal-neutron fission.For this reason,the mined ore must be enriched with $$^{235}U$$. Both $$^{235}U \ (T_{1/2} = 7.0 \times 10^8 \ y)$$ and $$^{238}U \ (T_{1/2} = 4.5 \times 10^9 \ y)$$ are radioactive. How far back in time would natural uranium ore have been a practical reactor fuel,with a $$^\dfrac{^{235}U}{^{238}U}$$ ratio of $$3.0 \%$$?
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Q2
In a sample of uranium the ratio of 238U and 235U by weight is 93 to 7%. The half-life of 238U and 235U are 4.5×109 and 7.13×108 year respectively. The contribution of radioactivity by both separately after a time interval of 108 year if 100 g sample is taken is :
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A $$200 \ MW$$ fission reactor consumes half its fuel in $$3.00 \ y$$. How much $$^{235}U$$ did it contain initially? Assume that all the energy generated arises from the fission of $$^{235}U$$ and that this nuclide is consumed only by the fission process.
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Some uranium samples from the natural reactor site were found to be slightly enriched in $$^{235}U$$, rather than depleted.Account for this in terms of neutron absorption by the abundant isotope $$^{238}U$$ and the subsequent beta and alpha decay of its products.
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Q5
Verify that, as reported in the above table, fissioning of the $$^{235}U$$ in $$1.0 \ kg$$ of $$UO_2$$ (enriched so that $$^{235}U$$ is $$3.0 \%$$ of the total uranium) could keep a $$100 \ W$$ lamp burning for $$690 \ y$$.

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