Chemistry - Radioactivity Question with Solution | TestHub

Question Explanation: Understanding successive radioactive decay

Concept: Successive decay and radioactive equilibrium

Solution: The rate of change of the number of nuclei of a daughter product is the difference between its formation rate and its decay rate. At equilibrium, the rate of formation equals the rate of decay, so the number of nuclei becomes constant.

For $\mathrm{A}\stackrel{{\lambda }_1}{\to }\mathrm{B}\stackrel{{\lambda }_2}{\to }\mathrm{C}$

at equilibrium all species will stop changing their amounts.

$\frac{-{\mathrm{dN}}_{\mathrm{A}}}{\mathrm{dt}}=\frac{{\mathrm{dN}}_{\mathrm{B}}}{\mathrm{dt}}$

also $\frac{-d{N}_A}{dt}={\lambda }_1{N}_A$ and $\frac{d{N}_B}{dt}={\lambda }_2{N}_B$

From above

${\lambda }_1{\mathrm{N}}_{\mathrm{A}}={\lambda }_2{\mathrm{N}}_{\mathrm{B}}$

$\frac{{\mathrm{N}}_{\mathrm{A}}}{{\mathrm{N}}_{\mathrm{B}}}=\frac{{\lambda }_2}{{\lambda }_1}$

Amount of B will increase and then decrease.

${\lambda }_2\gg {\lambda }_1$, B decays much faster then it is formed so equilibrium in achieved quickly.

Final Answer: B, C, and D are correct statements.