Question

8. Three grams of Bismuth-218 decay to 0.375 grams in one hour. What is the half-

Answer 1

Answer: 0.333 h

Explanation:

This problem can be solved using the Radioactive Half Life Formula:  

$A=A_{o}.2^{\frac{-t}{H}}$ (1)  

Where:  

$A=0.375 g$ is the final amount of the material  

$A_{o}=3 g$ is the initial amount of the material  

$t=1 h$ is the time elapsed  

$H$ is the half life of the material (the quantity we are asked to find)  

Knowing this, let's substitute the values and find $h$ from (1):

$0.375 g=(3 g)2^{\frac{-1h}{H}}$ (2)  

$\frac{0.375 g}{3 g}=2^{\frac{-1h}{H}}$ (3)  

Applying natural logarithm in both sides:

$ln(\frac{0.375 g}{3 g})=ln(2^{\frac{-1 h}{H}})$ (4)  

$-2.079=-\frac{1 h}{H}ln(2)$ (5)  

Clearing $H$:

$H=\frac{-1h}{-2.079}(0.693)$ (6)  

Finally:

$h=0.333 h$ This is the half-life of the Bismuth-218 isotope