Answer:
400 years
Explanation:
The equation that describes the decay of a radioactive sample is:
[tex]m(t)=m_0 (\frac{1}{2})^{t/t_{1/2}}[/tex] (1)
where
m(t) is the amount of sample left at time t
[tex]m_0[/tex] is the initial amount of the sample
[tex]t_{1/2}[/tex] is the half-life, which is the time taken for the sample to halve
In this problem we have:
[tex]t_{1/2}=100 y[/tex] is the half-life of Nickel-63
After a time t, the amount of sample left is 6.25% of the original one, which means that
[tex]\frac{m(t)}{m_0}=\frac{6.25}{100}[/tex]
So we can rewrite the equation (1) and solving for t to find the time:
[tex]\frac{6.25}{100}=(\frac{1}{2})^{t/t_{1/2}}\\\rightarrow \frac{t}{t_{1/2}}=4\\t=4t_{1/2}=4(100)=400 y[/tex]
