Question

I have an object that I want to know when it was made. I calculate that the object contains 0.12g of Iodine-131 but started with 60g. How old is my object?

Answer 1

Answer: 71.72 days

Explanation:

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

$A=A_{o}.2^{\frac{-t}{h}}$ (1)  

Where:  

$A=0.12 g$ is the final amount of Iodine-131

$A_{o}=60 g$ is the initial amount of Iodine-131

$t$ is the time elapsed  

$h=8 days$ is the half life of Iodine-131

Knowing this, let's substitute the values and find $t$ from (1):

$0.12 g=(60 g)2^{\frac{-t}{8 days}}$ (2)  

$\frac{0.12 g}{60g}=2^{\frac{-t}{8 days}}$ (3)  

Applying natural logarithm in both sides:

$ln(\frac{0.12 g}{60g})=ln(2^{\frac{-t}{8 days}})$ (4)  

$-6.21=-\frac{t}{8 days}ln(2)$ (5)

Finding $t$:

$t=71.72 days$