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 tand then decays in the time interval to t+ dt is given byP(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 toone.(b) Find an expression for the mean lifetime of the particle.(c) Find an expression for the probability that the particle lives for at leasttime T.

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Answered: 3. The lifetime of an unstable particle…

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