Since the half-life of 235U (7. 13 x 108 years) is less than that of 238U (4.51 x 109 years), the isotopic abundance of 235U has been steadily decreasing since the earth was fonned about 4.5 billion years ago. How long ago was the isotopic abundance of 235U equal to 3.0 a/o, the enrichment of the uranium used in many nuclear power plants

Explanation:

Given that:

The Half-life of = is less than that of

Although we are not given any value about the present weight of .

So, consider the present weight in the percentage of to be  y%

Then, the time elapsed to get the present weight of =

Therefore;

here;

= Number of radioactive atoms relating to the weight of y of

Thus:

--- (1)

However, Suppose the time elapsed from the initial stage to arrive at the weight of the percentage of to be =

Then:

 ---- (2)

here;

=  Number of radioactive atoms of relating to 3.0 a/o weight

Now, equating  equation (1) and (2) together, we have:

replacing the half-life of =

     ( since )

∴

The time elapsed signifies how long the isotopic abundance of 235U equal to 3.0 a/o

Thus, The time elapsed is