Decay Constant of Copper 66

In summary: And then you have to _use the graph_ to find the slope.It is a very commonly used technique to find a slope when you have a graph and don't know the equation of the line.That is why I suggested that you post the graph here, because we can't help you unless we can see the graph.I have drawn the graph and I have a straight line. I know how to find the slope but I do not understand how to use the data in the table to find the slope. What is the point of the table then?In summary, the conversation discusses an experiment where a sample of copper 66 is monitored for its decay rate over time. The data is recorded in a table and the relation between the count
  • #1
2
0

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


 
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  • #2
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.
 
  • #3
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...
 
  • #4
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.
 
  • #5
, 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.
 

1. What is the decay constant of Copper 66?

The decay constant of Copper 66 is a constant value that represents the rate at which this specific isotope undergoes radioactive decay. It is denoted by the symbol λ and has a value of approximately 0.000094 per year.

2. How is the decay constant of Copper 66 determined?

The decay constant of Copper 66 is determined through experiments that measure the rate of decay of this isotope over a period of time. This data is then used to calculate the decay constant using mathematical equations.

3. What factors can affect the decay constant of Copper 66?

The decay constant of Copper 66 can be affected by external factors such as temperature, pressure, and chemical reactions. It can also be influenced by the presence of other isotopes or elements, which can alter the rate of decay.

4. Why is the decay constant of Copper 66 important?

The decay constant of Copper 66 is important for understanding the behavior and properties of this isotope. It is also used in various fields of science, such as nuclear physics and geology, to determine the age of objects and study radioactive decay processes.

5. Can the decay constant of Copper 66 change over time?

The decay constant of Copper 66 is considered to be a constant value, meaning it does not change over time. However, in certain extreme conditions, such as in the presence of intense radiation or extreme temperatures, the decay constant may be slightly altered.

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