Question

You started with 64 g of a radioactive substance. If you have 4.0 g of that substance left, then how many half-lives have elapsed?

a.2
b.3
c.4
d.5

Answer 1

The answer would be 4 half lives. Hope this helps.

Answer 2

Answer: C) 4

Explanation: Half life is the time in which the amount of a radioactive substance remains halve of its initial amount. For example, half life of carbon-14 is 5730 years. It means if we have 4 grams of carbon-14 then it will remain 2 grams after 5730 years.

For the given problem, the initial amount of a radioactive substance is 64 grams, if 4.0 grams of that substance left, then how many half-lives have elapsed.

So, Its asking to calculate the number of half-lives. The formula used for this is:

`(A)/(A_0)=((1)/(2))^n`

where, A0 is the initial amount and A is final amount and n is the number of half-lives.

Let's plug in the values in the formula.

`(4.0)/(64)=((1)/(2))^n`

`(1)/(16)=((1)/(2))^n`

`((1)/(2))^4=((1)/(2))^n`

n = 4

So, there will be 4 half-lives and hence C is the correct choice.