Calc Nuclear Cross Section for Alpha Particles Reacting with 48-Ca

In summary, alpha particles fired at a thin target of calcium will produce protons. The total cross section is determined by the rate of initial alphas and the number of atoms in the target.
  • #1
Matt atkinson
116
1
1)
Alpha particles can react with 48-Ca to produce protons. Consider a beam of alpha particles of current 20nA fired at a think target of Ca of thickness $$1mg/cm^2$$. A detector subtending a solid angle of 4*10^-3 steradians, records 20 protons per second. Determine the total cross section (in mb) for the reaction. State any assumptions made.

2)

3)
So if I=20nA then the initial rate of alphas is:
$$R_o=\frac{I}{2e}=6.25 \times 10^{10} atoms / sec$$
And also the number of atoms in the think foil per $m^2$ is $$N=1.25\times 10^{23} atoms/m^2$$.
But I have no idea what to do from here I understand I'm given rate of initial alphas and rate of detection and a solid angle.
Could someone just point me in the right direction?
 
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  • #2
If the detector registers 20 protons per second, how many protons are produced in the target?
What is the rate of proton production in the target? (Or, more importantly, how does it relate to the cross section?)
 
  • #3
Assuming emission to be a semi-sphere and which is 2pi steradians then the protons per second created would be 31415 per second created so that means that there were that many reactions.
The only equation I can find is
$$\sigma = \frac{R}{I} $$
Reactions per second, over incident particles per second per unit area.
I know I calculated the number of alpha Per second but I don't quite understand how to get it per unit area and what the the number of 48-Ca atoms has to do with anything. I'm probably missing something simple.
 
  • #4
Oh if i instead workout the number of particles per uni cm^2 and then take the beam to have a area of 1cm^2 ?
 
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  • #5
Your final answer should not depend on the area of the beam. I suggest just calling the area A and making sure it cancels out from your final expression.
 
  • #6
I'm really quite stuck, hmm this is what I've done I just don't know how to put it together.

Let me know if the image can't be read, I will type my workings in latex.
ImageUploadedByPhysics Forums1426600456.547267.jpg
 
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1. What is nuclear cross section and why is it important in alpha particle reactions?

Nuclear cross section is a measure of the likelihood that a specific nuclear reaction will occur. In the case of alpha particle reactions with 48-Ca, it represents the probability that an alpha particle will interact with a 48-Ca nucleus. This measurement is important because it helps us understand and predict the behavior of nuclear reactions.

2. How is the nuclear cross section for alpha particles reacting with 48-Ca calculated?

The nuclear cross section for alpha particles reacting with 48-Ca is calculated by dividing the number of interactions between alpha particles and 48-Ca nuclei by the number of alpha particles present in the system. This value is then multiplied by the target thickness and the number of target nuclei per unit area to obtain the cross section in units of area.

3. What factors can affect the nuclear cross section for alpha particles reacting with 48-Ca?

Several factors can affect the nuclear cross section for alpha particles reacting with 48-Ca, including the energy of the alpha particle, the energy levels of the 48-Ca nucleus, and the angle at which the alpha particle approaches the 48-Ca nucleus. Additionally, the presence of other particles or fields can also influence the cross section.

4. How does the nuclear cross section for alpha particles reacting with 48-Ca differ from other types of nuclear reactions?

The nuclear cross section for alpha particles reacting with 48-Ca is specific to the reaction between these two particles. Other types of nuclear reactions, such as those involving protons or neutrons, will have different cross sections due to the varying characteristics of these particles and the nuclei they are interacting with.

5. What are some potential applications of understanding the nuclear cross section for alpha particles reacting with 48-Ca?

Understanding the nuclear cross section for alpha particles reacting with 48-Ca can have various applications, including in the design of nuclear reactors and understanding the behavior of nuclear waste. It can also be useful in fields such as nuclear medicine and astrophysics where alpha particle reactions play a role.

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