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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

349 years

b

540 years

c

380 years

d

 449 years

answer is A.

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Detailed Solution

Total{\text{ }}decay{\text{ }}constant{\text{ }}is\frac{1}{{1620}} + \frac{1}{{405}} = \frac{1}{{324}}

                                                  \frac{{No}}{4} = {N_0}{e^{ - \lambda \,t}}

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