Question

An element ${}_z{S}^A$ decays to ${}_{85}{R}^{222}$ after emitting $2\alpha$ particles and $1\beta$ particle. Find the atomic number and atomic mass of the element S.

Answer 1

On emission of $2$ alpha particles, mass number is reduced by $8$ and atomic number by $4$.

${}_z{S}^A{\to }_{z-4}{Q}^{A-8}+2{}_{2}H{e}^4$

Now, on emission of $1$ beta particle, mass number remains same but atomic number increases by $1$.

${}_{z-4}{Q}^{A-8}{\to }_{z-8}{R}^{A-8}+{}_{-1}^0\beta$

After decay, given element is ${}_{85}{R}^{222}$.

Therefore,

$A-8=222\Rightarrow A=230$

(Atomic Mass)

$Z-3=85\Rightarrow Z=88$

(Atomic Number)