Question

A half-life is the time it takes an amount of substance to decay to one-half of its original amount. For example, the sample is one-half after the first half-life but one-quarter (i.e., one-half of one-half) after the second half-life. If the half life of uranium-235 is 700 million years, how long does it take for 10.0 grams to decay to 2.5 grams? Express your answer in billions of years.

Answer 1

I’m failing to understand how it isn’t 1.4 billion years. From 10g to 5g would be 700 million years. Then, from 5g to 2.5g would be another 700 million years.

Answer 2

2.10 × 10⁹ yr

Step-by-step explanation:

The half-life of U-235 is the time it takes for half the U to decay.

After one half-life, half (50 %) of the original amount will remain.

After a second half-life, half of that amount (25 %) will remain, and so on.

We can construct a table as follows:

No. of Fraction Amount

half-lives t/(yr × 10⁶) remaining remaining/g

1 700 ½ 10.0

2 1400 ¼ 5.00

3 2100 ⅛ 2.50

4 2800 ¹/₁₆ 1.25

We see that 2100 × 10⁶ yr is three half-lives, and the amount of U-235 remaining is 2.50 g.

It takes 2.10× 10⁹ yr for the U-238 to decay to 2.50 g.