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)`

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:

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:

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:

The relation between half life T_(1//2) 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.

Two loops P and Q are made from a uniform wire. The radii of P and Q are R_(1) and R_(2) respectively and their moments of inertia are I_(P) and I_(Q) respectively. If (I_(P))/(I_(Q))=8 then (R_(1))/(R_(2)) is

If -((dN)/(dt))_(o) is the initial activity and -((dN)/(dt)) is the activity at time t in a radioactive disintegration then :