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Nuclear Decay Rate law

Posted: Thu Oct 29, 2009 11:19 pm
by Squirt
Ok so today, I was late for class so I missed like half of the crap...

I need to know how to solve this cause its like, a test on this crap tomorrow V.V
Tritium, is the radiocative isotope of Hydrogen (H-3) . It has a half life of 12.4 years. If 56.2 mg of Tritum are released from a nuclear power plant during the course of an accident, how much will remain after 60 years of the accident.

Using this formula
Image
Except that A is a K for Some reason..

Re: Nuclear Decay Rate law

Posted: Thu Oct 29, 2009 11:29 pm
by [SD]Master_Wong
logic says non but i know thats wrong because it halfs and halfs again not half gone then another half gone and leaving non, well interested to know the answer but seriously learn to do your homework your self, its what i do less i actually requires outside help ie surveys

Re: Nuclear Decay Rate law

Posted: Thu Oct 29, 2009 11:32 pm
by Squirt
[SD]Master_Wong wrote:logic says non but i know thats wrong because it halfs and halfs again not half gone then another half gone and leaving non, well interested to know the answer but seriously learn to do your homework your self, its what i do less i actually requires outside help ie surveys

I was there and took note through part of this.
I don't understand how to find Decay Constant..

After I find that out I can do rest,,

Re: Nuclear Decay Rate law

Posted: Thu Oct 29, 2009 11:34 pm
by lukefleming1
the best i can do for u is tell u what i think the answer might be using my own method
4.18mg will remain after the given time

60/12.4=4.84

56.2/2
Ans/2
Ans/2
Ans/2
Ans/2(1/.84)

Re: Nuclear Decay Rate law

Posted: Thu Oct 29, 2009 11:37 pm
by lukefleming1
lukefleming1 wrote:the best i can do for u is tell u what i think the answer might be using my own method
4.18mg will remain after the given time

60/12.4=4.84

56.2/2
Ans/2
Ans/2
Ans/2
Ans/2(1/.84)


but for some reason i don't think it is this simple
otherwise u wouldn't need natural logs to figure it out

Re: Nuclear Decay Rate law

Posted: Thu Oct 29, 2009 11:39 pm
by Squirt
lukefleming1 wrote:
lukefleming1 wrote:the best i can do for u is tell u what i think the answer might be using my own method
4.18mg will remain after the given time

60/12.4=4.84

56.2/2
Ans/2
Ans/2
Ans/2
Ans/2(1/.84)


but for some reason i don't think it is this simple
otherwise u wouldn't need natural logs to figure it out

No we did that yesterday, for this you do need natural logs.
Can't divide by 2 anymore =(

Re: Nuclear Decay Rate law

Posted: Thu Oct 29, 2009 11:40 pm
by lukefleming1
Squirt wrote:
lukefleming1 wrote:
lukefleming1 wrote:the best i can do for u is tell u what i think the answer might be using my own method
4.18mg will remain after the given time

60/12.4=4.84

56.2/2
Ans/2
Ans/2
Ans/2
Ans/2(1/.84)


but for some reason i don't think it is this simple
otherwise u wouldn't need natural logs to figure it out

No we did that yesterday, for this you do need natural logs.
Can't divide by 2 anymore =(


bah can't help u then my 10th grade math will only go so far xD

Re: Nuclear Decay Rate law

Posted: Thu Oct 29, 2009 11:46 pm
by lukefleming1
http://en.wikipedia.org/wiki/Exponential_decay
hate to refer u to wikipedia but honestly the equations halfway down the page seem to be related to finding ur decay constant
worth a shot anyways imo

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 12:59 am
by poehalcho
I can somehow see that this is incredibly simple...
I haven't actually had this kind of stuff, but here's my go...

60/ 12.4 = 4.84
56.2/(2^4.84) = 1.36 gr

if you wanna check it:
you know it halved approx. 5x
56/2 = 28
28/2 = 14
14/2 = 7
7/2 = 3.5
3.5/2 = 1.75

That number is very close to it! There's your answer!

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 1:39 am
by Squirt
poehalcho wrote:I can somehow see that this is incredibly simple...
I haven't actually had this kind of stuff, but here's my go...

60/ 12.4 = 4.84
56.2/(2^4.84) = 1.36 gr

if you wanna check it:
you know it halved approx. 5x
56/2 = 28
28/2 = 14
14/2 = 7
7/2 = 3.5
3.5/2 = 1.75

That number is very close to it! There's your answer!


I think thats wrong, you didn't find the constant..

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 1:45 am
by poehalcho
Squirt wrote:
poehalcho wrote:I can somehow see that this is incredibly simple...
I haven't actually had this kind of stuff, but here's my go...

60/ 12.4 = 4.84
56.2/(2^4.84) = 1.36 gr

if you wanna check it:
you know it halved approx. 5x
56/2 = 28
28/2 = 14
14/2 = 7
7/2 = 3.5
3.5/2 = 1.75

That number is very close to it! There's your answer!


I think thats wrong, you didn't find the constant..


Well you didn't ask for one -.-

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 1:50 am
by Squirt
poehalcho wrote:


Well you didn't ask for one -.-


I specifically remembered no more multiplying by 2.

It won't work for this..

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 3:54 am
by EvGa
You could set it up like this:

N = N(0)(1/2)^(t/h)
N = ?
N(0)= 56.2
t = 60
h = 12.4
N = 56.2(1/2)^(60/12.4)
N = 1.963991312 mg


Got that off yahoo answers.. don't know if it's correct. It's been two years since I've taken chemistry.

Doing a quick dirty calculation.. if you go through the half lifes until 10.6 years are left you get 1.75.. so not going the entire 12 years for the decay would cause you to have a little more.. 1.96 looks right.

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 11:44 am
by Kaigar
You're solving for N(t) = the ammount left at time t

All you need to do is plug in the variables you have been given.

λ = the half-life (keep it in the same units as you use for t, that is in years) = 12.4 years

N(0) = the ammount at time = 0 = 56.2mg in your case

ln = natural logarithm, i'm assuming you'll have access to a calculator and can use this function.

so,
ln[N(t)/56.2] = -12.4*60

applying some maths, [ ln(a/b) = ln(a)-ln(b) ]
ln[N(t)] - ln(56.2) = -744
ln[N(t)] = -739.971
e^{ln[N(t)]} = e^-739.971
N(t) = e^-739.971

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 12:34 pm
by Zypher
fuccn genoiss on the forums now

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 2:08 pm
by SM-Count
Kaigar wrote:You're solving for N(t) = the ammount left at time t

All you need to do is plug in the variables you have been given.

λ = the half-life (keep it in the same units as you use for t, that is in years) = 12.4 years

N(0) = the ammount at time = 0 = 56.2mg in your case

ln = natural logarithm, i'm assuming you'll have access to a calculator and can use this function.

so,
ln[N(t)/56.2] = -12.4*60

applying some maths, [ ln(a/b) = ln(a)-ln(b) ]
ln[N(t)] - ln(56.2) = -744
ln[N(t)] = -739.971
e^{ln[N(t)]} = e^-739.971
N(t) = e^-739.971

luls, lambda's the decay constant, not the half life. OP gonna fail.

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 4:39 pm
by EvGa
SM-Count wrote:luls, lambda's the decay constant, not the half life. OP gonna fail.


Haha, yep. Then there are also different equations for 0, first, and second order reactions..

Find K with equation: T = (-1/k)ln(2)

Where T is halflife.. so (-ln(2))/12.4 = -0.055898966

K = -0.055898966

Plug that into the original equation and see what ya get.

ln(Nt/56.2)= -(-0.055898966(12.4))

Solve for Nt.




I think, lol.

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 9:53 pm
by Kaigar
Hmmm... so where's the radioactive decay constant come from then? Do you need to derive it from the half-life some how?

Anyway, sorry if bad advise was bad.

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 9:57 pm
by Kaigar
ok, so lambda = log2/(half-life)

too late but....FFFUUU--

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 9:58 pm
by poehalcho
it's official...
srf sucks at chemistry...

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 9:59 pm
by Kaigar
This is physics

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 10:01 pm
by Squirt
Kaigar wrote:This is physics

No its Chemistry..

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 10:06 pm
by Kaigar
Semantics!

What level of study is this at? high school? university?

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 10:10 pm
by poehalcho
high school

Re: Nuclear Decay Rate law

Posted: Fri Oct 30, 2009 10:11 pm
by Squirt
Kaigar wrote:Semantics!

What level of study is this at? high school? university?

AP course, High school

Re: Nuclear Decay Rate law

Posted: Sat Oct 31, 2009 4:17 am
by Kagami
should ask a classmate :)