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 [tex]Q=Q_oe^{rt}[/tex]
Where, [tex]Q_o=250[/tex] 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. [tex]Q=\frac{Q_o}{2}[/tex]
Substitute in the formula,
[tex]\frac{Q_o}{2}=Q_oe^{r\times 15}[/tex]
[tex]\frac{1}{2}=e^{r\times 15}[/tex]
Taking log both side,
[tex]\log (\frac{1}{2})=r\times 15[/tex]
[tex]-0.301=r\times 15[/tex]
[tex]\frac{-0.301}{15}=r[/tex]
[tex]r=-0.02[/tex]
Now, we have to find Q in 100 minutes,
[tex]Q=Q_oe^{rt}[/tex]
Substitute in the formula,
[tex]Q=250e^{-0.02\times 100}[/tex]
[tex]Q=250e^{-2}[/tex]
[tex]Q=250\times 0.13[/tex]
[tex]Q=32.5[/tex]
Therefore, 32.5 grams will be left after 100 minutes.
