A radioactive material has mean lives of 1620 years and 660 years for α and β emissions respectively. The material decays by simultaneous α and β emission. The time in which 1 4 t h of the material re

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A radioactive material has mean lives of 1620 years and 660 years for α and β emissions respectively. The material decays by simultaneous α and β emission. The time in which 1 4 t h of the material remains intact is -

TestHub · Accepted Answer

Effective mean life for parallel disintegration is given by

$τ = \frac{τ_{1} τ_{2}}{τ_{1} + τ_{2}} = \frac{1620 \times 660}{2280} = 469 year$

Let t be the time in which ${1 / 4}^{t h}$ of the material remains intact

$\frac{N}{4} = \frac{N}{2^{\frac{t}{τ}}}$

$t = 2 τ l n 2$

$t = 2 \times 469 \times 0.693$

$t = 650$ year

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