A radioactive nucleus has mean life τ. What is the probability that it survives up to time τ but decays before time 3τ?
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Question

A radioactive nucleus has mean life τ. What is the probability that it survives up to time τ but decays before time 3τ?

G1 Physics · Accepted Answer

Survival probability up to time t is P(survive to t) = exp(−t ÷ τ). The probability of surviving to τ but not surviving to 3τ is P = exp(−1) − exp(−3). Numerically, exp(−1) ≈ 0.3679, exp(−3) ≈ 0.0498. Thus, P ≈ 0.3679−0.0498 = 0.3181. Therefore the closest option is 0.318. Correct option: C.