When {}_{92}U^{238} changes into {}_{82}Pb^{2 | vedclass

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(D) Let the number of $\alpha$-particles emitted be $n_{\alpha}$ and the number of $\beta^-$-particles emitted be $n_{\beta}$.In an $\alpha$-decay,the

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$8$ and $6$

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(D) Let the number of $\alpha$-particles emitted be $n_{\alpha}$ and the number of $\beta^-$-particles emitted be $n_{\beta}$.In an $\alpha$-decay,the mass number decreases by $4$ and the atomic number decreases by $2$. In a $\beta^-$-decay,the mass number remains unchanged and the atomic number increases by $1$.The change in mass number is $238 - 206 = 32$. Since only $\alpha$-decay affects the mass number,$4n_{\alpha} = 32$,which gives $n_{\alpha} = 8$.The change in atomic number is $92 - 82 = 10$. The net change in atomic number is given by $2n_{\alpha} - n_{\beta} = 10$.Substituting $n_{\alpha} = 8$,we get $2(8) - n_{\beta} = 10$,which implies $16 - n_{\beta} = 10$,so $n_{\beta} = 6$.Thus,$8$ $\alpha$-particles and $6$ $\beta^-$-particles are emitted.

When ${}_{92}U^{238}$ changes into ${}_{82}Pb^{206}$,the number of $\alpha$ and $\beta^-$ particles emitted are:

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