NEET Physics Nuclei Questions Solved

For a substance the average life for $\mathrm{\alpha }$-emission is 1620 years and for $\mathrm{\beta }$ emission is 405 years. After how much time the 1/4 of the material remains after $\mathrm{\alpha }$ and $\mathrm{\beta }$ emission

(a) 1500 years            (b) 300 years
(c) 449 years              (d) 810 years

(c) ${\mathrm{\lambda }}_{\mathrm{\alpha }}=\frac{1}{1620}$ per year and ${\mathrm{\lambda }}_{\mathrm{\beta }}=\frac{1}{405}$ per year and it is given that the fraction of the remained activity $\frac{\mathrm{A}}{{\mathrm{A}}_{0}}=\frac{1}{4}$
Total decay constant

We know that $\mathrm{A}={\mathrm{A}}_{0}{\mathrm{e}}^{-\mathrm{\lambda t}}⇒\mathrm{t}=\frac{1}{\mathrm{\lambda }}{\mathrm{log}}_{\mathrm{e}}\frac{{\mathrm{A}}_{0}}{\mathrm{A}}$

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