Question

MEDAL!!
How old is a sample of U-235 that has 3% left of the original amount? (HL for U-235 is 700 million years)

Answer 1

In general, the equation for half-life is:

\[m=m_0\left( 1 \over 2 \right)^{t \over t_{0.5}}\]
Where m(0) is your starting mass, m is the final mass, t is the total time elapsed, and t(0.5) is the length of the half-life. Since t/t(0.5) gives you the number of half-lives that occurred, all you're really doing is halving your starting mass as many times as there are half-lives.

The question tells us that m=0.03m(0), and the t(0.5) is 7 x 10^8 years. So, our equation becomes:

\[0.03m_0=m_0\left( 1 \over 2 \right)^{t \over7 \times 10^8}\]
Which is:\[0.03=\left( 1 \over 2 \right)^{t \over7 \times 10^8}\]
All you need to do is solve for t and you'll have your answer!