How Do You Calculate Radiation Count Rate for Different Energies?

[v_pino]

Homework Statement

I've attached the problem sheet and my attempt at the problem. I've completed all the parts except for the last part, where I have to calculate the count rate of the radioactive source. The answers should be 6000 counts for 185MeV and 4650 counts for 1MeV.

I'm not sure if it's simply 1000x6 for the 185MeV one. And I couldn't get the right answer for the 1MeV one.

Thank you.

Homework Equations

The Attempt at a Solution

 

[mfb]

Those 185keV-photons are absorbed quickly - the depth of the material (as seen by the detector) does not matter, only the surface area is relevant (this is different from your result). You can just multiply the number with 6 to get a good approximation.
If all photons would penetrate the material, the orientation of the bar would not matter.

For the 1MeV-photons, you have to take the depth into account: For an emission x cm away from the air (towards the detector), how many photons reach the detector? Can you integrate this over the whole material?

 

[v_pino]

Doesn't the mass attenuation coefficient take into account of a 3D source? Should I use it in the equation I=I_0 exp(-mu * x) ? Can I say that the final intensity I for case (A) is 1000? Then use this to find the initial intensity in case (A). Then assuming the initial intensity is same in (A) and (B), use it to find the final intensity in (B)? Using this method, I get 21600 counts which isn't correct.

 

[mfb]

Doesn't the mass attenuation coefficient take into account of a 3D source?

What do mean with that? I don't find an interpretation where the answer is "yes".

Should I use it in the equation I=I_0 exp(-mu * x) ?

That is the point of this coefficient.

Can I say that the final intensity I for case (A) is 1000?

Sure, that is given. That is not the I in your formula, however, as you don't have a constant x for all regions of the source.

 

[paranormal]

Hello,

I can provide some guidance on how to approach this problem. First, let's review the concept of radiation count rate. Count rate is the number of radiation events (such as decays or interactions) that occur in a given period of time. It is typically measured in counts per second (cps) or counts per minute (cpm).

In this problem, we are given a radioactive source with two different energies, 185MeV and 1MeV. We need to calculate the count rate for each of these energies. To do this, we need to use the formula:

Count rate = Number of events / Time

In this case, the number of events is given to us (6000 for 185MeV and 4650 for 1MeV) and we need to determine the time. To do this, we can use the information about the detector and the distance from the source.

From the problem sheet, we know that the detector has a diameter of 5cm and is located 10cm away from the source. This means that the detector is capturing radiation from a spherical surface with a radius of 10cm (since the detector is 5cm in diameter).

To calculate the time, we need to use the fact that radiation follows an inverse square law, meaning that the intensity of radiation decreases with the square of the distance from the source. This means that at a distance of 10cm, the intensity is 1/100 (10^2) of the intensity at the source. Therefore, the time needed to capture the same number of events at the detector is 100 times longer than the time needed at the source.

Putting this all together, we can calculate the count rate for the 185MeV source as follows:

Count rate = Number of events / Time

Count rate = 6000 / (Time at source x 100)

We know that the time at the source is 1 second, so the count rate is:

Count rate = 6000 / (1 x 100) = 60 cps

Similarly, for the 1MeV source, the count rate is:

Count rate = 4650 / (1 x 100) = 46.5 cps

I hope this helps you to understand how to approach this problem. Remember to always carefully consider the information given and use the appropriate formulas to solve the problem. Good luck with your homework!