Physics - Modern Physics Question with Solution | TestHub

The initial nucleus is ${}_{92}^{242}\mathrm{X}$.

The nuclear reaction involving the emission of two $\alpha$ particles (${}_2^4\mathrm{He}$), one electron (${}_{-1}^0\mathrm{e}$), and two positrons (${}_{+1}^0\mathrm{e}$) can be written as:

${}_{92}^{242}\mathrm{X}\to {}_{\mathrm{P}}^{234}\mathrm{Y}+2{}_2^4\mathrm{He}+1{}_{-1}^0\mathrm{e}+2{}_{+1}^0\mathrm{e}$

Conserving the atomic number (charge) on both sides of the reaction:

$92=\mathrm{P}+2(2)+1(-1)+2(+1)$

$92=\mathrm{P}+4-1+2$

$92=\mathrm{P}+5$

$\mathrm{P}=92-5=87$

Answer: 87