Chapter 11.3, Problem 58PPS

To determine

Find the amount of radon remain form an initial 60 grams after 4 weeks.

Answer to Problem 58PPS

0.9375 grams of radon remain from an initial 60 grams after 4 weeks

Explanation of Solution

Given:

Radon has a half − life of about 4 days. This means that about every 4 days, half of the mass of radon decays into another element. How many grams of radon remain from an initial 60 grams after 4 weeks?

Concept Used:

We have that there is 60 grams of random initial, so $a_1=60$

As about every 4 days, half of the mass of radon decays into another element and we have to calculate for 4 weeks.

  $n=\frac{4\text{weeks}}{4}=\text{1}\text{week}\text{=}\text{7}\text{days}\text{and}r\text{=}\text{0}\text{.5}$

So, we have to calculate $a_7$ by using the formula $a_n=a_1·r^{n-1}$

Calculation:

  $\begin{array}{l}{a}_1=60;r=0.50;n=7;\text{Find}{a}_7\\ a_n=a_1·r^{n-1}\\ $ a=60\cdot {(0.5)}^{-4}=60\cdot {(0.5)}^6=0.9375$\end{array}$

Therefore, 0.9375 grams of radon remain from an initial 60 grams after 4 weeks.

Thus, 0.9375 grams of radon remain from an initial 60 grams after 4 weeks.