Question regarding decay, protons and neutrons

[ezach1]

Homework Statement

[/B]
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 into 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??

Homework Equations

[/B]
t½=ln2
---
λ

The Attempt at a Solution

Im dying over here but I know I can do this. If anyone is willing to help me I am 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...

 

[mfb]

Which types of radioactive decay do you know? Which one could be relevant here?

I believe Madeupium would be the decay product because it has decayed to 51 protons.

What about the neutrons?

Im still working on the rest smh...

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.

 

[ezach1]

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

 

[ezach1]

Which types of radioactive decay do you know? Which one could be relevant here?
.

Im not quite sure what you mean??

 

[mfb]

The neutrons are the same for madeupium

51 and 52 are the same?

Im not quite sure what you mean??

I'm not sure how that question can be unclear.

 

[ezach1]

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

 

[ezach1]

It can't be beta decay because the protons are higher in both elements

 

[mfb]

It can't be beta decay because the protons are higher in both elements

There are two types of beta decay.

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

 

[ezach1]

There are two types of beta decay.

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

Gotcha...beta plus and minus.

 

[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.

 

[mfb]

Correct.

 

[ezach1]

thanks for your help...you wouldn't believe how much it means to me..

Now for the second part...this ones a doozy..I don't even know which equation would be best. I see Log, etc.

t/½= ln2/λ

 

[mfb]

See above.

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.