• Minkowski
In summary, Thomas is seeking help with a problem involving the relationship between paper thickness and radiation intensity. He has measured the coefficient and has a graph showing a linear decline in intensity with increasing paper thickness. However, he is unsure of how to use this information to determine the thickness of the paper. After discussing the data and potential errors, it is suggested that fitting the data to an exponential decay curve may provide a more accurate solution. Thomas realizes that his graph was printed on "exp-paper" and uses the equation ln(2)/T½ to find the value of k and solve the problem.
Minkowski
Hello,

This is my first post here, and I must say I'm in trouble caused by the last problem in my homework assignment. I live in Denmark so excuse me if some of the terms are not correct English.

What I do know: Source: Ti-204, Decay: Beta-, Activity: 3,1MBq,
Half-life period: 3,8 years

The relationship between paperthickness (x) and intensity (measured decay/sec) is declining linearly (not sure what it's called). I've measured a, the coefficient, to: -40 counts/mm.

The problem is this: At a measurement 25 months after the source started decaying, the detector measures 478 decays/sec.
- What is the thickness of the paper?

I am troubled because I'm not sure of the relationship between the measured decay (Intensity) and the other parametres. I know what the activity should be, but not the intensity.

Any help would be appreciated.

/Thomas M.

I think you have left out some information. There must have been a detector count at the beginning of the 25 month. The usual relationship between radiation intensity and barrier thickness assumes that the fractional change in count is proportional to the thickness. If a certain thickness reduces the intensity by 10%, a second layer would reduce the lowered intensity by another factor of 10% for a net reduction of 19%. Intensity vs thickness is analogous to intensity vs time.

OlderDan said:
I think you have left out some information. There must have been a detector count at the beginning of the 25 month. The usual relationship between radiation intensity and barrier thickness assumes that the fractional change in count is proportional to the thickness. If a certain thickness reduces the intensity by 10%, a second layer would reduce the lowered intensity by another factor of 10% for a net reduction of 19%. Intensity vs thickness is analogous to intensity vs time.

I've got a graph: 805 counted decays at the beginning of the 25 months. This graph is declining linearly with a = -40 counts/mm.
e.g. 765 counts at 1 mm. paper, 725 at 2 mm. and so forth. What do I do with that info.? I think it's my understanding of measured intensity (counts/time), or lack thereof, that is the main problem. What say you?

/Thomas M.

Minkowski said:
I've got a graph: 805 counted decays at the beginning of the 25 months. This graph is declining linearly with a = -40 counts/mm.
e.g. 765 counts at 1 mm. paper, 725 at 2 mm. and so forth. What do I do with that info.? I think it's my understanding of measured intensity (counts/time), or lack thereof, that is the main problem. What say you?

/Thomas M.
I would say that your graph is probably not really linear. Surely the data points you fit to find the slope of the line had some scatter, and you drew the best straight line you could through those points. What do you think you would have found if the source intensity had been 205 counts instead of 805 counts? Do you think you would have seen 165 at 1mm, 125 at 2mm and so forth? What is far more likely is that you would have seen the same fractional reduction in intensity, or 195 at 1mm, and 185 at 2mm etc.

If you still have your original data, try fitting it to an exponential decay curve instead of a line. The form of the equation will be

I = I_o*exp(-kx) where I_o is the source intensity and x is paper thickness.

If you don't have all the data, you can still use the couple of points you just quoted to find the k in this equation. Once you have that, calculate the intensity of your source after 25 months and calculate the ratio of measured intensity to source intensity. That ratio should be the same for a given thickness of paper no matter how strong the source. If you find the value of k from your original data, you can find x from the intensity ratio measured at any time.

OlderDan said:
I would say that your graph is probably not really linear. Surely the data points you fit to find the slope of the line had some scatter, and you drew the best straight line you could through those points. What do you think you would have found if the source intensity had been 205 counts instead of 805 counts? Do you think you would have seen 165 at 1mm, 125 at 2mm and so forth? What is far more likely is that you would have seen the same fractional reduction in intensity, or 195 at 1mm, and 185 at 2mm etc.

If you still have your original data, try fitting it to an exponential decay curve instead of a line. The form of the equation will be

I = I_o*exp(-kx) where I_o is the source intensity and x is paper thickness.

If you don't have all the data, you can still use the couple of points you just quoted to find the k in this equation. Once you have that, calculate the intensity of your source after 25 months and calculate the ratio of measured intensity to source intensity. That ratio should be the same for a given thickness of paper no matter how strong the source. If you find the value of k from your original data, you can find x from the intensity ratio measured at any time.

I've made a big mistake: I wasn't aware that the graph was printed on "exp-paper", that's why it made a straight line. :yuck:
I should have known this, since I made an experiment 2 weeks ago, that resulted in an exponential declining function.

I know that k = ln(2)/T½
I know both ln(2) obviously, and as stated before T½ = 3,8 years. Thank you for the help!

/Thomas.

Minkowski said:
I've made a big mistake: I wasn't aware that the graph was printed on "exp-paper", that's why it made a straight line. :yuck:
I should have known this, since I made an experiment 2 weeks ago, that resulted in an exponential declining function.

I know that k = ln(2)/T½
I know both ln(2) obviously, and as stated before T½ = 3,8 years. Thank you for the help!

/Thomas.
I know what you mean, but in this case k is related to thickness rather than time. There is a "half-thickness" if you will that reduces the intensity to half its original value, analogous to the "half-life" that reduces the source intensity by half as time passes. You might label the half-thickness as X½.

OlderDan said:
I know what you mean, but in this case k is related to thickness rather than time. There is a "half-thickness" if you will that reduces the intensity to half its original value, analogous to the "half-life" that reduces the source intensity by half as time passes. You might label the half-thickness as X½.

Yep, I am aware of that. The problem recided in the proper use of intensity - I wasn't sure if the 805 counts/sec. should be understood as intensity. You've been a great help,

Thanks alot.

## 1. What is paper thickness measured by radiation?

Paper thickness measured by radiation is a non-destructive technique that uses radiation, such as X-rays or gamma rays, to determine the thickness of paper. It is commonly used in the paper industry to ensure uniformity and quality control of paper products.

## 2. How does paper thickness measured by radiation work?

The technique works by passing a beam of radiation through the paper material and measuring the amount of radiation that is absorbed or scattered. This data is then used to calculate the thickness of the paper based on the known properties of the material and the radiation source.

## 3. Is paper thickness measured by radiation safe?

Yes, paper thickness measured by radiation is considered safe as the radiation used is very low and does not pose any health risks. However, proper safety precautions and regulations should always be followed when using any type of radiation.

## 4. What are the advantages of using paper thickness measured by radiation?

One of the main advantages is that it is a non-destructive technique, meaning the paper does not need to be cut or damaged in any way during the measurement process. It is also a quick and accurate method for measuring paper thickness, making it ideal for quality control purposes.

## 5. Are there any limitations to paper thickness measured by radiation?

One limitation is that the technique is only suitable for measuring the thickness of thin materials, such as paper. It may not be accurate for measuring the thickness of thicker materials or materials with high levels of density variations. Additionally, specialized equipment and trained personnel are needed to perform the measurements.

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