Determine the value of a decay constant

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Homework Help Overview

The discussion revolves around determining the decay constant for C-14, given its half-life of 5730 years. Participants are exploring the relationship between half-life and decay constant, as well as the appropriate units for the decay constant.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to set up the decay formula based on the half-life and are questioning the correct application of the formula. There is confusion regarding the representation of half-life in the equation and the values to be used.

Discussion Status

Some participants have provided guidance on how to approach the problem, including clarifying the meaning of the half-life in terms of remaining nuclei. There is ongoing exploration of the formula setup and the implications of using different values.

Contextual Notes

Participants have noted that this is an early assignment in the semester, and some are unsure about the concepts as they have not yet been covered in class. There is also mention of the need to express the decay constant in appropriate MKS units.

Kingyou123
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Homework Statement



What's up guys, I'm stuck on #2 of this worksheet,http://luc.edu/faculty/dslavsk/courses/phys111/homework/phys111-2015hw1.pdf
The half - life of C - 14 is 5730 years. Determine the value of its decay constant (and express the answer in appropriate MKS units).

2.The attempt at a solution
I'm not sure if I'm doing this correctly , but I set up my formula like this , 5730=14e-(constant of decay)5730
 
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Kingyou123 said:

Homework Statement



What's up guys, I'm stuck on #2 of this worksheet,http://luc.edu/faculty/dslavsk/courses/phys111/homework/phys111-2015hw1.pdf

2.The attempt at a solution
I'm not sure if I'm doing this correctly , but I set up my formula like this , 5730=14e-(constant of decay)5730
Hello . Welcome to PF !

You will get a better response if you display the question so that it can be read directly. The following is what I was able to obtain from your pdf file using Window's "Snipping Tool" & easily display here.
upload_2015-8-26_20-13-4.png


Better yet, you could type out the problem. I makes it easier to respond to, and it shows initiative on your part.

As far as your attempt at a solution goes, it looks like you simply picked out some numbers at random from the problem statement and then plugged them into the given equation.
 
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SammyS said:
Hello . Welcome to PF !

You will get a better response if you display the question so that it can be read directly. The following is what I was able to obtain from your pdf file using Window's "Snipping Tool" & easily display here.
View attachment 87850

Better yet, you could type out the problem. I makes it easier to respond to, and it shows initiative on your part.

As far as your attempt at a solution goes, it looks like you simply picked out some numbers at random from the problem statement and then plugged them into the given equation.
I've been using this fourm. https://www.physicsforums.com/threads/decay-constant.24169/ , as a guide and I can't figure out what to do... it's the first assignment of the semester and we haven't gone over this...
 
Kingyou123 said:
I've been using this forum. https://www.physicsforums.com/threads/decay-constant.24169/ , as a guide and I can't figure out what to do... it's the first assignment of the semester and we haven't gone over this...
C-14 is carbon 14. That's just an identifier for the type of nucleus being addressed. The number 14, will not be involved anywhere in the solution.

The problem statement gives many hints, maybe even telling you much of what you need to do to solve the problem.

If you start with N0 C-14 nuclei, then after 5730 years (one half-life), how many C-14 nuclei remain in your sample?

That quantity is what you put in for N(5730) .
 
SammyS said:
C-14 is carbon 14. That's just an identifier for the type of nucleus being addressed. The number 14, will not be involved anywhere in the solution.

The problem statement gives many hints, maybe even telling you much of what you need to do to solve the problem.

If you start with N0 C-14 nuclei, then after 5730 years (one half life), how many C-14 nuclei remain in your sample?

That quantity is what you put in for N(5730) .
Omg, you just made it so easy... so the formula would be 5370=(.5)e^(-(decay)5370) or would I set the entire thing to zero?
 
Kingyou123 said:
Omg, you just made it so easy... so the formula would be 5370=(.5)e^(-(decay)5370) or would I set the entire thing to zero?
No.

And you didn't answer the main question I asked..

If you start with N0 nuclei, then how many will remain after one half-life has elapsed?
 
SammyS said:
No.

And you didn't answer the main question I asked..

If you start with N0 nuclei, then how many will remain after one half-life has elapsed?
Half of the N0 nuclei would remain.
 
Kingyou123 said:
Half of the N0 nuclei would remain.
Correct.

That's what goes on the left hand side of the equation.
 
SammyS said:
Correct.

That's what goes on the left hand side of the equation.
So the formula would start looking like this .5=(.5)e^-(decay)5730
 
  • #10
Kingyou123 said:
So the formula would start looking like this .5=(.5)e^-(decay)5730
How did you get that?

Where does the .5 come from on both sides?

Isn't the left side N0/2 , and the right side N0 times the exponential ?
 
  • #11
SammyS said:
How did you get that?

Where does the .5 come from on both sides?

Isn't the left side N0/2 , and the right side N0 times the exponential ?
I assumed that .5 is half, I get confused when I don't enter values in. So No/2=N0e^-(decay)5730? The thing that confuses me is what values to put in the fourmla that I have now.
 
  • #12
Kingyou123 said:
I assumed that .5 is half, I get confused when I don't enter values in. So No/2=N0e^-(decay)5730? The thing that confuses me is what values to put in the fourmla that I have now.
You should use another set of parentheses to make that technically correct.

0.5⋅N0=N0e^(-(decay)5730) .

Just solve for the decay constant. First step is to divide both sides by N0 . Right ?
 
  • #13
SammyS said:
You should use another set of parentheses to make that technically correct.

0.5⋅N0=N0e^(-(decay)5730) .

Just solve for the decay constant. First step is to divide both sides by N0 . Right ?
Okay I divided both sides by No and then took the natural log of both sides. Afterwards I divided by -5730 to get my answer, correct?
 
  • #14
Kingyou123 said:
Okay I divided both sides by No and then took the natural log of both sides. Afterwards I divided by -5730 to get my answer, correct?
Yes, but 5730 is in units of years. That gives you the decay constant in units of years-1. MKS would be in units of seconds-1.
 

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