$U^{238}$ 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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Obtain the maximum kinetic energy of $\beta$-particles and the radiation frequencies of $\gamma$-decays in the decay scheme shown in the figure. You are given that:
$m(^{198}Au) = 197.968233 \; u$
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$A$ radioactive nucleus undergoes $\alpha$-emission to form a stable element. What will be the recoil velocity of the daughter nucleus if $V$ is the velocity of $\alpha$-emission and $A$ is the atomic mass of the radioactive nucleus?

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