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Q.

The mean lives of a radioactive substance are 1620 years and 405 years for α -emission and  β-emission respectively. The time during which three fourth of a sample will decay if it is decaying both by α -emission and  β-emission simultaneously.

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a

449 years

b

349 years

c

249 years

d

149 years

answer is A.

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Detailed Solution

Total decay constant is λ=1τ1+1τ2=11620+1405=1324sec-1 t=1λln4=324×ln4=449 yr
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