Question

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

life of this isotope?

Answer 1

Answer: 0.333 h

Step-by-step explanation:

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

`A=A_(o).2^{(-t)/(H)}` (1)

Where:

`A=0.375 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^{(-1h)/(H)}` (2)

`(0.375 g)/(3 g)=2^{(-1h)/(H)}` (3)

Applying natural logarithm in both sides:

`ln((0.375 g)/(3 g))=ln(2^{(-1 h)/(H)})` (4)

`-2.079=-(1 h)/(H)ln(2)` (5)

Clearing
`H`:

`H=(-1h)/(-2.079)(0.693)` (6)

Finally:

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