The atomic weight of thorium is $A = 232$ and the atomic number is $Z = 90$. After disintegration,the final element obtained is $Pb$,which has $A = 208$ and $Z = 82$. In this process,the number of emitted $\alpha$ and $\beta$ particles are:

$A$ nucleus of atomic mass $A$ and atomic number $Z$ emits a $\beta^-$ particle. The atomic mass and atomic number of the resulting nucleus are

$A$ $^{238}U$ nucleus decays by emitting an $\alpha$ particle of speed $v \ m/s$. The recoil velocity of the residual nucleus is (in $m/s$):

$_6^{12}C$ absorbs an energetic neutron and emits a beta particle. The resulting nucleus is

$A$ radio nuclide $A_1$ with decay constant $\lambda_1$ transforms into a radio nuclide $A_2$ with decay constant $\lambda_2$. If at the initial moment the preparation contained only the radio nuclide $A_1$,then the time interval after which the activity of the radio nuclide $A_2$ reaches its maximum value is:

When an element ${}_{90}^{232}Th$ decays into ${}_{82}^{208}Pb$, the number of $\alpha$ and $\beta^{-}$ particles emitted respectively are