Mixed in with , uranium mined today contains 0.72% of fissionable , too little to make reactor fuel for thermal-neutron fission. For this reason, the natural uranium must be enriched with . Both , , and , , are radioactive. We have to calculate how far back in time would natural uranium have been a practical reactor fuel, with a ratio of 3.0%.

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As the half-life of is , its disintegration constant is

and as the half-life of is , its disintegration constant is

Let the total number of at time be and those of then be .

Let the number of , t years later, that is at present, be and those of , t years later, be .

From the radioactive decay law, we note that

We are given that

We thus have the relation