3. The lifetime of an unstable particle is governed by the exponential probabil- ity distribution. In particular, the probability that the particle lives for time t and then decays in the time interval to t+ dt is given by P(1) dt = e¬M a dr, where A is a positive decay constant. (a) Show that the probability that the particle eventually decays is equal to one. (b) Find an expression for the mean lifetime of the particle. (c) Find an expression for the probability that the particle lives for at least time T.
3. The lifetime of an unstable particle is governed by the exponential probabil- ity distribution. In particular, the probability that the particle lives for time t and then decays in the time interval to t+ dt is given by P(1) dt = e¬M a dr, where A is a positive decay constant. (a) Show that the probability that the particle eventually decays is equal to one. (b) Find an expression for the mean lifetime of the particle. (c) Find an expression for the probability that the particle lives for at least time T.
Related questions
Question
Transcribed Image Text:3. The lifetime of an unstable particle is governed by the exponential probabil-
ity distribution. In particular, the probability that the particle lives for time t
and then decays in the time interval to t+ dt is given by
P(1) dt = e¬M a dr,
where A is a positive decay constant.
(a) Show that the probability that the particle eventually decays is equal to
one.
(b) Find an expression for the mean lifetime of the particle.
(c) Find an expression for the probability that the particle lives for at least
time T.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 5 images
