# Homework Help: Question regarding decay, protons and neutrons

1. Oct 24, 2015

### ezach1

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

You find a 1kg piece of rock containing 3 elements:
Fakium with 50 protons and 52 neutrons
imaginium with 52 protons and 48 neutrons
madeupium with 51 protons and 51 neutrons
Fakium is known to be radio active, Which of the other two elements could be the decay product and why?
On January 1st 2016 at 9am, you take a piece of the rock in to the lab and measure that it is comprised of 0.5kg of fakium, 0.2kg imaginium, and 0.3kg madeupium. Exactly 24 hours later, you do the same measurement and find that the mass of fakium is now 0.48kg. What is the half life of fakium?
How long will it take until there is only 0.1kg of fakium left in the rock??

2. Relevant equations

t½=ln2
---
λ

3. The attempt at a solution
Im dying over here but I know I can do this. If anyone is willing to help me Im willing to help myself too.
I believe Madeupium would be the decay product because it has decayed to 51 protons.
Im still working on the rest smh...

2. Oct 24, 2015

### Staff: Mentor

Which types of radioactive decay do you know? Which one could be relevant here?
What about the neutrons?
If you know the initial amount and the half-life, how can you calculate how much is left after some time t? The same formula works for the other direction, known remaning mass but unknown half-life.

3. Oct 24, 2015

### ezach1

The neutrons are the same for madeupium, but imaginium has 52 protons

4. Oct 24, 2015

### ezach1

Im not quite sure what you mean??

5. Oct 24, 2015

### Staff: Mentor

51 and 52 are the same?
I'm not sure how that question can be unclear.

6. Oct 24, 2015

### ezach1

Gamma, Alpha , Beta..
51 and 52 arent the same...i apologize

7. Oct 24, 2015

### ezach1

It cant be beta decay because the protons are higher in both elements

8. Oct 25, 2015

### Staff: Mentor

There are two types of beta decay.

(You can edit your posts if you want to add something, by the way).

9. Oct 25, 2015

### ezach1

Gotcha...beta plus and minus.

10. Oct 25, 2015

### ezach1

i say its madeupium and I believe it has undergone beta 4 decay.The numbers of protons and neutrons in an atom's nucleus change during beta decay, the total number of particles (protons + neutrons) remains the same.

11. Oct 25, 2015

### Staff: Mentor

Correct.

12. Oct 25, 2015

### ezach1

thanks for your help...you wouldnt believe how much it means to me..

Now for the second part...this ones a doozy..I dont even know which equation would be best. I see Log, etc.

t/½= ln2/λ

Last edited: Oct 25, 2015
13. Oct 25, 2015

See above.