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Chapter 38: Problem 2
Why are there no stable nuclei for sufficiently high atomic numbers?
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In the liquid-drop model, the mass of a nucleus with mass number \(A\) can be expressed as a quadratic in \(Z: M(A, Z)=\) \(c_{1} A-c_{2} Z+\left(c_{2} A^{-1}+c_{3} A^{-1 / 3}\right) Z^{2},\) where the \(c s\) are constants determined from experimental data. Show that the value of \(Z\) that gives the minimum mass (not necessarily an integer) is \(Z_{\min }=\) \((A / 2) /\left[1+\left(c_{3} / c_{2}\right) A^{2 / 3}\right] .\) (Note: A plot of \(Z_{\min }\) versus \(N=A-Z\) gives the line of greatest nuclear stability in Figs. 38.3 and \(38.12 .\) )
Nitrogen- 13 is a 10 -min-half-life isotope used to "tag" ammonia for PET scans, including quantification of myocardial infarction. Consider an intravenous injection incorporating \(20 \mathrm{mCi}\) of \(\mathrm{N}-13\) Plot a graph of \(\mathrm{N}-13\) activity versus time, with your vertical axis logarithmic and your horizontal axis linear. Why is the graph a straight line? What's the significance of its slope?
Beta decay by positron emission is soon followed by a pair of 511 -keV gamma rays. Why?
Compare the radius of the proton (the \(A=1\) nucleus) with the Bohr radius of the hydrogen atom.
A \(^{235} \mathrm{U}\) nucleus undergoes neutron-induced fission, yielding "Iti Cs, three neutrons, and another nucleus, What's that nucleus?
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