Question

Asample arginally contained 10^​20 radioactive atoms,which emit alpha particles.The ratio of alpha particles emitted in third year to thatemitted during second year is 0.3.how many alpha particles are emitted in first year?

Answer 1

$$\begin{gathered} Theformulaofradioactivedecayisgivenby, \\ N=N_0{e}^{-\lambda t} \\ Aspergivendata,wehave \\ {N}_1={10}^{20}{e}^{-\lambda }-----\left(1\right) \\ {N}_2={10}^{20}{e}^{-2\lambda }-----\left(2\right) \\ {N}_3={10}^{20}{e}^{-3\lambda }-----\left(3\right) \\ But\frac{N_3}{N_2}=0.3=e^{-\lambda } \\ Therefore{N}_1={10}^{20}{e}^{-\lambda }={10}^{20}\times 0.3=3\times {10}^{19}alphaparticles. \end{gathered}$$