Two species of radioactive atoms are mixed in equal number. The disintegration of the first species is `lambda` and of the second is `lambda`/3. After a long time the mixture will behave as a species with mean life of approximately

Options

A. `(0.70)/(lamda)`
B. `(2.10)/(lamda)`
C. `(1.00)/(lamda)`
D. `(0.52)/(lamda)`

Answer

B

Explanation

Avg life `= (int t dN_(1) + tdN_(2))/(2N_(0)) rArr dN_(2)= (lamda)/(3) N_(0) e^((-lamda t)/(3)) dt`
Avg life `= (underset(0)overset(oo)int t(lamda N_(0) e^(-lamda t) dt + (lamda)/(3) N_(0) e^((-lamda t)/(3)) dt))/(2N_(0))`
On Integration, we get
Average life `= (2)/(lamda) ~~ (2.10)/(lamda)`