Question

answer the following questions and show your work in the space provided. 1. the half - life of radium - 226 is 1600 years. how many grams of a 0.25g sample will remain after 4800 years? 2. sodium - 24 has a half - life of 15 hours. how much sodium - 24 will remain in an 18.0g sample after 60 hours? 3. $^{24}$na has a half - life of 15 hours. if you have 15000mg of $^{24}$na how much will remain after 45 hours? 4. carbon - 14 has a half - life of 5730 years. if you start out with 900 mg of $^{14}$c, how much will you have after 3 half - lives? 5. $^{6}$he has a half - life of.08 seconds. if you have 5000.mg of $^{6}$he, how much will remain after.32 seconds? 6. after 42 days a 2.0 g sample of phosphorus - 32 contains only 0.25g of isotope. what is the half - life of phosphorus - 32?

Explanation:

1.

Step1: Calculate number of half - lives

The number of half - lives $n=\frac{4800}{1600}=3$.

Step2: Use half - life formula

The amount remaining $A = A_0\times(\frac{1}{2})^n$, where $A_0 = 0.25$ g. So $A=0.25\times(\frac{1}{2})^3$.
$A = 0.25\times\frac{1}{8}=0.03125$ g.

Step1: Calculate number of half - lives

The number of half - lives $n=\frac{60}{15}=4$.

Step2: Use half - life formula

The amount remaining $A = A_0\times(\frac{1}{2})^n$, where $A_0 = 18.0$ g. So $A=18.0\times(\frac{1}{2})^4$.
$A = 18.0\times\frac{1}{16}=1.125$ g.

Step1: Calculate number of half - lives

The number of half - lives $n=\frac{45}{15}=3$.

Step2: Use half - life formula

The amount remaining $A = A_0\times(\frac{1}{2})^n$, where $A_0 = 15000$ mg. So $A=15000\times(\frac{1}{2})^3$.
$A = 15000\times\frac{1}{8}=1875$ mg.

Answer:

$0.03125$ g

2.