How many and - particles are emitted in the trasmutation _ 90 ^ 2…

Question

How many $\alpha$ and $\beta$ - particles are emitted in the trasmutation
$
{ }_{90}^{232} Th \longrightarrow{ }_{82}^{208} Pb
$

✓

Answer

$
{ }_{90}^{232} Th \longrightarrow{ }_{82}^{208} Pb
$
The emission of one $\alpha$-particle decreases the mass number by 4 whereas the emission of $\beta$-particles has no effect on mass number.
Net decrease in mass number $=232-208=24$.
This decrease is only due to $\alpha$-particles. Hence, number of $\alpha$-particles emitted $=\frac{24}{4}=6$
Now, the emission of one $\alpha$-particle decrease the atomic number by 2 and one $\beta$-particle emission increases it by 1 .
The net decrease in atomic number $=90-82=8$
The emission of $6 \alpha$-particles causes decrease in atomic number by 12 .
However, the actual decrease is only 8 . Thus, atomic number increases by 4 . This increase is due to emission of $4 \beta$-particles.
Thus, $6 \alpha$ and $4 \beta$-particles are emitted.

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