half-life chemistry problem?

Question

If sodium-24 has a half-life of 15 hr, what is the activity of the sodium after 2 1/2 days? i dont understand half lifes or how to solve them...

Answer 1

2.5 days = 60 hours
60/15 = 4
therefore, Na-24 will undergo 4 half-lives (if that is the right plural form of it).
so after 2.5 days, Na-24 will be (1/2)^4 = 1/16 compared to the original.

Answer 2

The activity is proportional to number of atoms that remain undecayed in the sample
Activity = (decay constant) x (number of undecayed atoms)

You will have seen a graph with the formula N = No e^( - B t )
where N is the number of undecayed atoms, No is the number of atoms at the start, and B is the decay constant (usually lambda)

This is a model of how many atoms are left undecayed at a specific time

You will also probably have done an experiment with lots of dice, removing all of the ones with a 6 etc after each throw.

The more dice (atoms) there are, the more are likely to get a 6 (decay) each time.

A half life of the dice model is the number of throws taken to get rid of half of the dice

While the number of dice goes down, the chance of getting a 6 does not, so the same proportion should get a 6 each throw

A half life of a sample of metal is the time taken for half of the nuclei to decay

This can be found on the graph by the time taken for the y value to get to half of its current point.

2.5 days is 60 hours, which is 4 half lives.
So the activity at the end will have halved 4 times compared to the beginning
=1/2 x 1/2 x 1/2 x 1/2
=1/16 of the initial activity

only 1/16 of the number of atoms that you started with will not have decayed.