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

Step-by-step explanation:

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

`A=A_(o).2^{(-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^{(-t)/(8 days)}` (2)

`(0.12 g)/(60g)=2^{(-t)/(8 days)}` (3)

Applying natural logarithm in both sides:

`ln((0.12 g)/(60g))=ln(2^{(-t)/(8 days)})` (4)

`-6.21=-(t)/(8 days)ln(2)` (5)

Finding
`t`:

`t=71.72 days`