# Homework Help: Finding Mass of Isotope After Radioactive Decay by Half-Life

1. Feb 6, 2013

### rakeru

1. The problem statement, all variables and given/known data

A radioactive sample contains 2.25g of an isotope with a half-life of 3.8 days.
How much of the isotope in grams will remain after 11.0 days?

2. Relevant equations

3. The attempt at a solution

Hi! I've just started college this semester. I'm taking Introductory Chemistry. Right now we are doing nuclear chemistry. This problem is confusing, though, because I'm not sure if I can just divide the half-life like a normal number.. My professor doesn't teach. Literally.

I tried doing this problem this way:

It starts off with 2.25g.
After 3.8 days (one half-life) it's 1.125g.
After 7.6 days (two half lives) it's 0.5625g.
But in another half-life, 11.4 days would have passed. More than 11. In 11.4 days it would be 0.28125g.

Is this correct? How would I calculate this? My book doesn't tell me.. Is there a specific way? It only tells me that it's "beyond the scope of this book". Please help!

Last edited: Feb 6, 2013
2. Feb 6, 2013

### tiny-tim

welcome to pf!

hi rakeru! welcome to pf!
in other words, after 3.8n days it's 2.25 times 1/2n

so after n days it's 2.25 times 1/2n/3.8

so you need to find 211/3.8

3. Feb 7, 2013

### rakeru

Hi!!

So I was looking up similar questions previously and it turns out that one person said the same thing as you.

I tried it first with others just in case and it worked. :D

I did: 2.25g × 1/211/3.8

And I got 0.302537977g.

The question had also told me to give the answer in three significant figures so: 0.303g, right?

Uhm, I hope it works! I'm going to submit my answer now.. :) Thank you so much!

4. Feb 7, 2013

### tiny-tim

hi rakeru!
yup, looks fine!

5. Feb 7, 2013

### rakeru

Yup! I got it right :) Thank you.