Half-Life Question: Thorium-234 (24 days)

[kingbryant]

Homework Statement

Thorium-234 has a half life of 24 days. If you begin with a 280 kg sample, in how many days will you have 17.5 kg of Thorium left?

Homework Equations

DONT KNOW EQUATIONS

The Attempt at a Solution

DONT KNOW HOW TO START. I AM CONFUSED

 

[G01]

You must know SOMETHING. Sorry, but you have to show some work. It's the rules. Finding the relevant equation would be a start. It shouldn't be too hard, especially if you have a book for the course.

 

[kingbryant]

i know halflife is the amount of time it takes for half of the atoms in a sample to decay. i don't know how to find the answer or how to start it up. this is a topic that doesn't have examples/questions in the book. my teacher gave this question for a project. he said to do find it out so i need to know how to do it to fully understand

 

[Sleek]

You may follow this method. You still have to work on the problem though.

Now, you are going to end up on 17.5 kg. If you keep on halving the initial 280 kg, you'll at some time reach 17.5. Or the other way round, you could proceed in the forward direction. If you keep on doubling 17.5, you'll reach 280 at some point. Both of them end up in the same equation.

Can you find the number of Halving it has to undergo to reach the final state? Then you have to multiply it by 24 (as it is the half life period, since Total Time = No. of halving required x Half life period). And you have your answer.

Regards,
Sleek.

 

[Mr. Mathmatics]

You technically have enough information to start right there. As Sleek said you may do it manually. For example...

In 0 days 280 grams
In 24 days you will have 140
etc.,

It may end up though that the numbers of days may not be a multiple of 24 which means you may end up doing a bit of work. I don't want to give away the answer so remember you may want to set up a constant equation for this problem.

 

[G01]

Yes you could do it manually as you mentioned above.

To get you started on a more formal method, here's the wikipedia article and the hyperphysics article on half life. Pay attention to the exponential decay equation. and the decay constant and how it relates to the half-life. It's no textbook, but it's a start:

http://en.wikipedia.org/wiki/Half-life

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/halfli.html