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For a substance the average life for α-emission is 1620 years and for β emission is 405 years. After how much time the 1/4 of the material remains after α and β emission

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1500 years

300 years

449 years

810 years

answer is C.

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Detailed Solution

per year and

per year and it is given that the fraction of the remained activity

Total decay constant

\lambda = {\lambda _\alpha } + {\lambda _\beta } = \frac{1}{{1620}} + \frac{1}{{405}} = \frac{1}{{324}}per\,year

We Know that

A = {A_0}{e^{ - \lambda t}} \Rightarrow t = \frac{1}{\lambda }{\log _e}\frac{{{A_0}}}{A}

t = \frac{1}{\lambda }{\log _e}4 = \frac{2}{\lambda }{\log _e}2

= 324 x 2 x 0.693 = 449 years.

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