In a radioactive material the activity at time t1 is R1 and at a later time t2, it is R2. If the decay constant of the material is , then
- R1 = R2
- R1 = R2 e- (t1 - t2)
- R1 = R2 e (t1 - t2)
- R1 = R2(t2/t1).
Answer
(2) R1 = R2 e- (t1 - t2)
Solution
Activity decreases exponentially with time: R = R0 e- t
⇒ R1 = R0 e- t1 and R2 = R0 e- t2
⇒ R1R2 = e- (t1 - t2)
∴ R1 = R2 e- (t1 - t2)
(Check: t1 < t2, so the exponent is positive and R1 > R2, as expected.)
Answer: (2)