1.

If lambda is decay constant of a nucleus, find the probability that a nucleus will decay in time t and further will not decay in time t:

Answer»

`(1-e^(lambdat))^(-1), e^(-lambdat)`
`(1-e^(-lambdat)), e^(-lambdat)`
`e^(-lambdat), (1-e^(-lambda t))`
`(e^(-lambdat))^(-1), (1-e^(-lambdat))`

Solution :Number of ATOMS that decay in time `t=N_(0)=N_(0) e^(-lambdat)`
`=N_(0) (1-e^(-lambda t)`
Probability that ATOM decays in time
`t=("Number of atoms decayed")/("Total number of the atoms")`
`=(N_(0) (1-e^(-lambda t)))/(N_(0))`
`=1-e^(-lambda t) ..........(1)`
Probability that an atom will not decay in time
`t=1-(1-e^(-lambdat))`
`=e^(-lambda t) ..........(2)`


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