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.