$U^{238}$ decays into $Th^{234}$ by the emission of an $\alpha$-particle. There follows a chain of further radioactive decays,either by $\alpha$-decay or by $\beta$-decay. Eventually,a stable nuclide is reached,and after that,no further radioactive decay is possible. Which of the following stable nuclides is the end product of the $U^{238}$ radioactive decay chain?
- A$Pb^{206}$
- B$Pb^{207}$
- C$Pb^{208}$
- D$Pb^{209}$
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For the $\beta^{+}$ (positron) emission from a nucleus,there is another competing process known as electron capture (an electron from an inner orbit,say,the $K$-shell,is captured by the nucleus and a neutrino is emitted).
$_{z}^{A} X + e^{-} \rightarrow _{z-1}^{A} Y + \nu$
Show that if $\beta^{+}$ emission is energetically allowed,electron capture is necessarily allowed,but not vice-versa.
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Show that if $\beta^{+}$ emission is energetically allowed,electron capture is necessarily allowed,but not vice-versa.
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