Nuclear Activity: Estimating Time of Production

In summary, the conversation discusses the estimation of time required to produce a 100 μCi source of 36Cl by irradiating 1g of natural nickel chloride in a neutron flux of 1014 cm-2s-1. The equation used to calculate the time is provided, along with the necessary values for the variables. The solution is confirmed to be correct by a scientist, and the person is encouraged to ask for further clarification if needed.
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Didn't really have any idea when I started to write the problem, but I think I've managed to work it out now posting for clarification.

Homework Statement



Estimate the time it will take to produce a 100 μCi source of 36Cl by irradiating 1g of natural nickel chloride (molecular weight 129.6) in a neutron flux of 1014 cm-2s-1. The cross section for neutron capture on 35Cl is 43 b and the half-life of 36Cl is 3 x 105 years. 75.8% of natural chlorine consists of 35Cl.

Homework Equations



Number of 35-Cl atoms in 1g of NaCl2 is
[tex] N = 2x0.758xN_A/molecular weight = 7.04x10^{21} [/tex]
[tex]A(t) = \lambda N = P(1 - e^{-\lambda t} \approx P\lambda t[/tex]
[tex]t = \frac{A(t)}{P\lambda} = \frac{A(t)t_{1/2}}{ln 2 x \Omega x F x N} [/tex]

[tex]F = incident flux, A(t) = activity, \Omega = cross section for neutron capture[/tex]

The Attempt at a Solution



[tex] F = 10^{14} cm^{-2}s^{-1} [/tex]
[tex]t_{1/2} = 3.16x10^7 x 3x10^5 = 9.48x10^12 s [/tex]
[tex]\Omega = 43x10^-24 cm [/tex]
[tex]A(t) = 100\mu Ci = 3.7x10^6 Bq [/tex]

Putting in the numbers gives 1.67164x10^6 seconds = 19.35 days

Didn't really have any idea when I started to write the problem, but I think I've managed to work it out now posting for clarification.
 
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  • #2


Hi there! I can confirm that your solution is correct. The equation you used to calculate the time it will take to produce a 100 μCi source of 36Cl is the correct one, and you have correctly plugged in all the necessary values. Great job on figuring it out! Let me know if you have any further questions or need any more clarification. Keep up the good work!
 

Related to Nuclear Activity: Estimating Time of Production

1. How is the time of production for nuclear activity estimated?

The time of production for nuclear activity is estimated using a method called radiometric dating. This involves measuring the amount of radioactive isotopes present in a sample and comparing it to the known rate of decay for that isotope. The age of the sample can then be calculated based on this information.

2. What types of isotopes are used in estimating the time of production for nuclear activity?

There are several types of isotopes that can be used in estimating the time of production for nuclear activity. Some common examples include carbon-14, uranium-238, and potassium-40. Each isotope has a different half-life, which is the amount of time it takes for half of the atoms in a sample to decay.

3. How accurate is the estimated time of production for nuclear activity?

The accuracy of the estimated time of production for nuclear activity depends on several factors, including the type of isotope used, the quality of the sample, and the analytical techniques used. In general, radiometric dating can provide fairly accurate results, with an error range of about 1-2%.

4. Can the estimated time of production for nuclear activity be affected by external factors?

Yes, external factors such as contamination or environmental changes can affect the accuracy of the estimated time of production for nuclear activity. This is why it is important to carefully select and prepare samples, as well as use multiple analytical techniques to confirm results.

5. What other methods are used to estimate the time of production for nuclear activity?

In addition to radiometric dating, other methods such as dendrochronology (tree ring dating), ice core dating, and varve chronology (sediment layer dating) can also be used to estimate the time of production for nuclear activity. These methods rely on different types of evidence and can provide complementary information.

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