Question
Question: The mean lives of a radioactive substance are 1620 year and 405 year for a-emission and b-emission r...
The mean lives of a radioactive substance are 1620 year and 405 year for a-emission and b-emission respectively. Find the time during which three-fourth of a sample will decay if it is decaying both by a-emission and b-emission simultaneously.
A
249 years
B
449 years
C
133 years
D
99 years
Answer
449 years
Explanation
Solution
The decay constant l is the reciprocal of the mean life t. Thus, la = 16201 per year and
lb = 4051per year \Total decay constant, l = la + lb or
l = 16201+4051=3241 per year
We know that N = N0 e–lt When 43 th part of the sample has disintegrated, N = N0/4
\ = N0e–lt or elt = 4 Taking logarithm of both sides, we get lt = loge 4 or t = λ1loge 22 = λ2 loge 2
= 2 × 324 × 0.693 = 449 year