How Do You Calculate the Decay Constant of Copper 66?

[SarahM975]

Homework Equations

I was given all this information... I cannot figure it out whatsoever. I would post my attempts but there were too many. Any ideas would be helpful. I know the answer is 5.09 as the half life
Decay Constant of Copper 66



Sources do not emit radiation at a constant rate but fade away with time.

In this experiment, you monitor the count rate of a sample of copper 66 which has just been prepared.

The detector counts for one minute at each interval.


time(minutes) counts
0 ------------932
1 -------------813
2 -------------710
3 -------------619
4------------ 540
5------------ 453
6 ------------435
-
time(minutes) counts
7 ---------359
8 -----------318
9 ---------266
10 ----------239
11 ----------205
12 ------------182
13 ------------161

time(minutes) counts
14 ------------138
15 ------------121
16 --------------108
17 ------------92
18-------------- 80
19 ------------70
20 ------------61




The data in the table should satisfy the relation:

N=N0e-(lambda)t
where, N0 = the number of counts at time 0

N = the number of counts after an elapsed time T

lambda = the decay constant for the specific isotope

t = the elapsed time


Plot the count rate vs the time on semilog paper using the data found in the table. Calculate the slope.
Hint#1: Make sure you calculate the slope in the right units and that the sign of the answer make sense.

Hint#2: From the formula above the value of the slope will be "-lambda"

Be sure to enter the answer in the summary table in your lab outline.

The half-life, T, is defined as the time for the count rate to drop by a factor of 2.

(1/2)N0 = N0e^-(lambda)T
T = 0.693/lambda

Homework Statement

i cannot find the half life/slope

Homework Equations

equations above

The Attempt at a Solution

my attempts were not posted because it would make this uber long

 

[Delphi51]

Welcome to PF, Sarah.
So, you have a graph but can't find its slope?
Put "how to find the slope of a graph" into Google.
If you scan your graph and post it here, we can help you with it.
It will be easiest if you do the graph with a spreadsheet. Just capture the window with alt+printScreen, paste into a paint program, save and upload. Uploading to a service like Photobucket works really well. Then you can paste an IMG link here.

If that is too much work, tell us the coordinates of two points on your line of best fit.

 

[SarahM975]

Yes, I know how to find the slope but can I not find it with the equations I have and the information I have, or else there would be no point to this assignment because I am in University so...I doubt they would just ask me to find the slope...

 

[Delphi51]

Plot the count rate vs the time on semilog paper using the data found in the table. Calculate the slope.
Hint#1: Make sure you calculate the slope in the right units and that the sign of the answer make sense.

Hint#2: From the formula above the value of the slope will be "-lambda"

Yes, they HAVE just asked you to find the slope!
Of course you have to draw the graph on log paper to get a straight line.

 

[asteriatic]

, but here is my explanation and solution:

To find the decay constant of copper 66, we will use the formula N=N0e-(lambda)t, where N0 is the initial number of counts, N is the number of counts after a certain elapsed time t, and lambda is the decay constant.

We can rearrange this formula to solve for lambda:

lambda = (ln(N0/N))/t

Using the given data, we can plug in the values for N0 and N at each time interval and the elapsed time t (1 minute) to calculate the decay constant.

For example, at time 0, N0 = 932 and N = 932. Plugging these values into the formula, we get:

lambda = (ln(932/932))/1 = 0

We can do this for each time interval and calculate the corresponding decay constant. Once we have all the values, we can take the average to get a more accurate decay constant for copper 66.

Alternatively, we can plot the count rate vs time on semilog paper and calculate the slope of the line. As mentioned in the hint, the slope of the line will be equal to -lambda. We can then use the formula T = 0.693/lambda to calculate the half-life of copper 66. The half-life is the time it takes for the count rate to drop by a factor of 2.

In this case, the slope of the line is approximately -5.09. Therefore, the decay constant for copper 66 is 5.09 minutes^-1. Using the formula T = 0.693/lambda, we can calculate the half-life to be approximately 0.136 minutes.

I hope this helps and clarifies the process of finding the decay constant and half-life for copper 66.