Question

The half–life of rubidium–89 is 15 minutes. If the initial mass of the isotope is 250 grams, how many grams will be left after 100 minutes?

Answer 1

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.

Answer 2

M(100) = 2.46 grams    .