Register to reply 
PLEASE HELP! Radioactive decay 
Share this thread: 
#1
Jan2113, 06:13 PM

P: 10

I've just been really thrown off by what this problem is asking me.
Given: The decay of a radioactive material may be modeled by assuming that the amount A(t) of material present (in grams) at time t (minutes) decays at a rate proportional to the amount present, that is dA/dt= kA for some positive constant k. Every subpart of this question refers to exactly the same radioactive material. Question: a. derive an equation for the amount A(t) present at time t in terms of the constant k and the amount A(o) present at time t=0 b. if A(5) = 1/3A(3), find K c. at what time t will the amount A(t) be 1/4A(0) My attempt (?): for part a I wasnt sure if it was referring to just giving the equation A(t)=A(0)e^kt and I have no idea how to go about b or c. please help me if possible ! I think i'm over thinking the problem. I'm just really thrown off by the lack of numbers. Thank you! 


#2
Jan2113, 06:19 PM

HW Helper
P: 6,207

For part a, you were given dA/dt = kA, you need to solve this first order DE to derive the equation you want. Are you able to do this?
For part b), once you have the formula from part a, you just need to substitute the numbers. For example A(1) means the value of A when t=1. 


#3
Jan2113, 06:22 PM

Mentor
P: 21,215

A(t)=A(0)e^(kt) Substitute these expressions into the the equation A(5) = (1/3)A(3) and solve for k. For the last one, you should have gotten the value of k in part b, so you should be able to do it by then. 


#4
Jan2113, 06:23 PM

P: 10

PLEASE HELP! Radioactive decay



#5
Jan2113, 06:30 PM

P: 10




#6
Jan2113, 06:53 PM

Mentor
P: 21,215

For part a, it appears that you need to derive the equation you showed, not just merely write it down. This entails solving the diff. eqn. dA/dt = kA.
This equation is fairly simple to solve, using separation of variables, one of the first techniques that you learn in diff. equations. dA/dt = kA => dA/A = k dt Part b assumes that you have a formula (function) for A(t). Use the formula to find A(5) and A(3), and substitute these values into the equation A(5) = (1/3) A(3). 


#7
Jan2113, 07:12 PM

P: 10

I got the equation the way you said to, but the problem doesn't give me any values for A(0), A(3), or A(5). And this is really confusing me. This problem has been stumping me for a long time because it doesn't give me much to work with. Sorry if i'm bugging you!



#8
Jan2113, 07:19 PM

Mentor
P: 21,215




#9
Jan2113, 07:24 PM

P: 10

I had dA/dt=kA and rearranged it and integrated both sides to get to the equation A(t)=A(0)e^(kt). now I know I'm supposed to plug the values for A(5) and A(3) into part b to solve for k, but how do I get those values if I don't know A(0) or k.



#10
Jan2113, 07:32 PM

Mentor
P: 21,215

What is A(5)?
What is A(3)? 


#11
Jan2113, 07:37 PM

P: 10

the only thing that they give me towards figuring that out is that A(5)=(1/3)A(3)... ? Not sure if that's what you meant. I wouldn't be able to solve for them using the equation for part a without knowing K or A(0).



#12
Jan2113, 07:47 PM

Mentor
P: 21,215

You have a formula for A(t). Evaluate your formula at t = 5 and t = 3. What do you get? 


#13
Jan2113, 09:56 PM

P: 10

Okay so I think I understand ! If I set A(5)=(1/3)A(3) in the equations then the A(0) values cancel and I can solve for k=(ln 3)/2.. hope that's right!



#14
Jan2113, 10:24 PM

HW Helper
Thanks
PF Gold
P: 7,575




#15
Jan2113, 10:31 PM

P: 10




#16
Jan2113, 10:38 PM

P: 10

okay so it looks like what I'm getting for part b is k= (ln 3)/2 ....? Is this right or am I completely off.



#17
Jan2113, 11:45 PM

Mentor
P: 21,215

You have a mistake, but you're on the right track.



#18
Jan2113, 11:54 PM

P: 10

it's the negative sign, right? I noticed that.



Register to reply 
Related Discussions  
Radioactive Decay  Introductory Physics Homework  4  
Nuclear Chemistry: Kinetics of Radioactive Decay and Radioactive Dating  Biology, Chemistry & Other Homework  1  
What is the proper use and meaning of Radioactive decay ? How much decay HAS occured  General Physics  2  
Radioactive decay equilibrium when decay constants are equal  Biology, Chemistry & Other Homework  2  
Radioactive Decay  Calculus  2 