Answer:
32.5 grams will be left after 100 minutes.
Step-by-step explanation:
Given : The half–life of rubidium–89 is 15 minutes. If the initial mass of the isotope is 250 grams.
To find : How many grams will be left after 100 minutes?
Solution :
Let the exponential equation of rubidium is \(Q=Q_oe^{rt}\)
Where, \(Q_o=250\) is the initial value
t is the time taken i.e. t=15 minutes
The half–life of rubidium–89 is 15 minutes.
i.e. \(Q=\frac{Q_o}{2}\)
Substitute in the formula,
\(\frac{Q_o}{2}=Q_oe^{r\times 15}\)
\(\frac{1}{2}=e^{r\times 15}\)
Taking log both side,
\(\log (\frac{1}{2})=r\times 15\)
\(-0.301=r\times 15\)
\(\frac{-0.301}{15}=r\)
\(r=-0.02\)
Now, we have to find Q in 100 minutes,
\(Q=Q_oe^{rt}\)
Substitute in the formula,
\(Q=250e^{-0.02\times 100}\)
\(Q=250e^{-2}\)
\(Q=250\times 0.13\)
\(Q=32.5\)
Therefore, 32.5 grams will be left after 100 minutes.
