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cortiver
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Homework Statement
\(From a past exam paper)
Na-24 can be produced by irradiation of 27-Al with energetic neutrons. It decays by beta emission.
An aluminium sample of mass m=0.2g was irradiated by energetic neutrons for a period of 1 hour. Two hours after the end of irradiation the total 24-Na activity of the sample was 295 Bq.
(i) Calculate the total number of Na-24 nuclei that were present in the aluminium sample immediately at the end of the irradiation.
(ii) What was the neutron flux (use a reaction cross-section of [tex]\sigma[/tex]=0.125 barns).
Homework Equations
Basically, when the sample is being irradiated the number of 24-Na atoms [tex]N^{*}[/tex] obeys
[tex]\frac{dN^{*}}{dt} = R - \lambda N^{*}[/tex]
where [tex]R = N\sigma \Phi[/tex] is the rate of neutron absorption, [tex]N[/tex] is the number of atoms in the sample, [tex]\sigma[/tex] is the microscopic cross-section, and [tex]\Phi[/tex] is the neutron flux. [tex]\lambda[/tex] is the decay constant. Once the irradiation is stopped, it decays according to
[tex]\frac{dN^{*}}{dt} = -\lambda N^{*}[/tex].
The Attempt at a Solution
It seems to be just a simple plug-and-chug question based on the rudimentary treatment of neutron activation analysis that we did in class, but the thing is that I can't see how you can possibly do it without knowing the Na-24 half-life and the atomic mass of aluminium, and neither of these values were given anywhere in the exam paper. Am I missing something obvious here?
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