Question

An elements ${}_{\mathrm{z}}\mathrm{S}^{\mathrm{A}}$ decay to ${}_{85}\mathrm{R}^{222}$ after emitting $2\mathrm{\alpha }$ particles and $1\mathrm{\beta }$ particles. Find the atomic number

and atomic mass of the elements $\mathrm{S}$.

Answer 1

Step1. Given data

No. of emitting $\mathrm{\alpha }$- particle is $2$.

No. of emitting $\mathrm{\beta }$- particle is $1.$

We known that one $\mathrm{\alpha }$- particles $\left({}_2{}^4\mathrm{He}^{}\right)$ decay decreases its mass number by $4$ units and number protons decrease by $2$ units:

Also one $\mathrm{\beta }$- particles decay does not effect on its mass number but proton number increase by one units .

Step2. Write the equation

${}_{\mathrm{z}}\mathrm{S}^{\mathrm{A}}\to {}_{85}\mathrm{R}^{222}+2·{}_2{}^4\mathrm{He}^{}+{}_{-1}{}^{°}\mathrm{\beta }\to \left(1\right)$

Step3. Finding atomic mass number

mass number of ${}_{85}\mathrm{R}^{222}$ is $222units.$

mass number of ${}_{\mathrm{Z}}\mathrm{S}^{\mathrm{A}}$ is $Aunits.$

Also from the equation $\to \left(1\right)$

$$\begin{gathered} 222=A-2\times 4+1\times 0 \\ A=222+8=230units. \end{gathered}$$.

Step4. Finding atomic number

Atomic Number of ${}_{\mathrm{Z}}\mathrm{S}^{\mathrm{A}}$ is Z

From the equation $\to \left(1\right)$

$$\begin{gathered} 85=Z-2\times 2+1\times 1 \\ Z=85+4-1 \\ =88units. \end{gathered}$$

Hence, Atomic number$88units.$ and Atomic mass number $230units$ of the elements $\mathrm{S}$.( that is ${}_{88}\mathrm{S}^{230}$).