Answer
(a) $\,\,^{131}_{53}I\rightarrow \,^{131}_{54}Xe+\,^{0}_{-1}e$
(b) 12.2 days
Work Step by Step
(a) Beta particle is nothing but an electron. When it is emitted, the new nuclide formed has the mass number but the atomic number is increased by 1. The nuclide with atomic number 54 and mass number 131 is $\,^{131}_{54}Xe$. The balanced equation is
$\,\,^{131}_{53}I\rightarrow \,^{131}_{54}Xe+\,^{0}_{-1}e$
(b) Recall that $\ln(\frac{A_{0}}{A})=kt=\frac{0.693}{t_{1/2}}\times t$
$\implies \ln(\frac{100}{35})=1.0498=\frac{0.693}{8.04\,d}\times(t)$
$\implies t=\frac{1.0498\times8.04\,d}{0.693}=12.2\,d$
