Question

Sodium-24 has ahalf-life of about 15 hours how much of an 1.60 gram sample of sodium-24 will remain after 60.0 hours? Ans :(1g)?

Answer 1

`0.1 g`

Explanation:

As we start with 1.6 grams and we know that 60 hours have passed, this equals 4 half-lives. This means that the weight of the sample has effectively been halved 4 times:

`(0.5)^4`

So simply multiply this with the mass:

`(0.5)^4 times 1.6=0.1 g`

Generally:
Remaining mass`=(0.5)^n times m`

Where `n` is the number of half-lives passed and `m` is the original mass of the sample.

Answer 2

There seems to be a mistake in your given answer.
The correct answer is `0.10" g"`

Explanation:

A formula for half-life decay is:

`A(t) = A(0)(1/2)^(t/t_(1/2))`

Where `t_(1/2)` is the half-life, t is the elapsed time (in the same time units as the half-life), `A(t)` is the amount of the radioactive substance remaining after the elapsed time, `A(0)` is the amount of the radioactive substance at the start of the elapsed time.

We are given that `A(0) = 1.60" g"`, `t_(1/2) = 15" hrs"` and `t = 60" hrs"`

`A(60" hrs") = 1.60" g"(1/2)^((60" hrs")/(15" hrs"))`

`A(60" hrs") = 1.60" g"(1/2)^4`

`A(60" hrs") = (1.60" g")/(16)`

`A(60" hrs") = (0.10" g")`