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For a radioactive material, its activity...

For a radioactive material, its activity `A` and rate of change of its activity of `R` are defined as `A=(-dN)/(dt)` and `R=(-dA)/(dt)`, where `N(t)` is the number of nuclei at time `t`. Two radioactive source `P` (mean life `tau`) and `Q` (mean life `2 tau`) have the same activity at `t=0`. Their rates of activities at `t=2 tau` are `R_(p)` and `R_(Q)`, respectively. If `(R_(P))/(R_(Q))=(n)/(e )`, then the value of `n` is:

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For a radioactive meterial , its activity A and rate of charge of its activity R are defined as A = - (dN)/(dt) and R = -(dA)/(dt) where N(t) is the number of nuclei at time t .Two radioactive source P (mean life tau ) and Q(mean life 2 tau ) have the same activity at t = 2 tau R_(p) and R_(Q) respectively , if (R_(p))/(R_(Q)) = (n)/(e)

For a radioactive meterial , its activity A and rate of charge of its activity R are defined as A = - (dN)/(dt) and R = (dA)/(dt) where N(t) is the number of nuclei at time I .Two radioactive source P (mean life tau ) and Q(mean life 2 tau ) have the same activity at t = 2 tau R_(p) and R_(Q) respectively , if (R_(p))/(R_(Q)) = (n)/(e)

The relation between half-life T of a radioactive sample and its mean life tau is:

The relation between half-life T of a radioactive sample and its mean life tau is:

A radioactive sample having N nuclei has activity R. Write down an expression for its half life in terms of R and N.