Physics

Problem

The thorium radioactive series starts with

^{232}_{90}\text{Th}

and ends with the stable nuclide

^{208}_{82}\text{Pb}

, proceeding only through

\alpha

-decays and

\beta^{-}

-decays. (i) Let

n_{\alpha}

and

n_{\beta}

be the respective numbers of

\alpha

and

\beta^{-}

particles emitted in the entire chain. Derive two simultaneous equations connecting

n_{\alpha}

and

n_{\beta}

with the changes in mass number and atomic number between the initial and final nuclei. (ii) Solve these equations to obtain the numerical values of

n_{\alpha}

and

n_{\beta}

. (iii) Substitute your results back into the two conservation statements to show explicitly that both mass number and atomic number are conserved. a. (i) Derive simultaneous equations for

n_{\alpha}

and

n_{\beta}

b. (ii) Solve for

n_{\alpha}

and

n_{\beta}

c. (iii) Verify conservation with the obtained values

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