A radioactive species has decay constant of `lambda=10^(-2)s^(-1)`. Probability that a particular nucleus decays in time t is p. Draw a graph showing variation of `rho` with t. Assume that the selected nucleus survives till last.

If lambda is the decay constant of a nucleus, find the propability that a nucleus wil decay in time t and will not decay in time t .

If m g of a radioactive species (molar mass M) has decay constant lambda The specis activity of sample at t = is given by:

A radioactive element A decays with a decay constant lambda . The fraction of nuclei that decayed at any time t , if the initial nucle are N_(0) is given by:

A radioactive nucleus X decays to a nucleus Y with a decay constant lambda_X=0.1s^-1, Y further decays to a stable nucleus Z with a decay constant lambda_Y=1//30s^-1 . Initially, there are only X nuclei and their number is N _0=10^20 . Set up the rate equations for the populations of X, Y and Z. The population of Y nucleus as a function of time is given by N_Y(t)={N _0lambda_X//(lambda_X-lambda_Y)}[exp(-lambda_Yt)-exp(-lambda_Xt)]. Find the time at which N_Y is maximum and determine the population X and Z at that instant.

A radioactive nucleus X decays to a nucleus Y with a decay constant lambda_X=0.1s^-1 , Y further decays to a stable nucleus Z with a decay constant lambda_Y=1//30s^-1 . Initially, there are only X nuclei and their number is N _0=10^20 . Set up the rate equations for the populations of X, Y and Z. The population of Y nucleus as a function of time is given by N_Y(t)={N _0lambda_X//(lambda_X-lambda_Y)}[exp(-lambda_Yt)-exp(-lambda_Xt)] . Find the time at which N_Y is maximum and determine the population X and Z at that instant.

A radioactive nucleus X decays to a nucleus Y with a decay constant lambda_X=0.1s^-1 , Y further decays to a stable nucleus Z with a decay constant lambda_Y=1//30s^-1 . Initially, there are only X nuclei and their number is N _0=10^20 . Set up the rate equations for the populations of X, Y and Z. The population of Y nucleus as a function of time is given by N_Y(t)={N _0lambda_X//(lambda_X-lambda_Y)}[exp(-lambda_Yt)-exp(-lambda_Xt)] . Find the time at which N_Y is maximum and determine the population X and Z at that instant.

A radioactive isotope X decays into a stable nucleus Y. Draw graphs showing the variation of rate of formation of Y versus time and the variation of population of Y versus time. Initial population of Y is zero.

A radioactive nucleus X decay to a nucleus Y with a decay with a decay Concept lambda _(x) = 0.1s^(-1) , gamma further decay to a stable nucleus Z with a decay constant lambda_(y) = 1//30 s^(-1) initialy, there are only X nuclei and their number is N_(0) = 10^(20) set up the rate equations for the population of X^9) Y and Z The population of Y nucleus as a function of time is givenby N_(y) (1) = N_(0) lambda_(x)l(lambda_(x) - lambda_(y))) (exp(- lambda_(y)1)) Find the time at which N_(y) is maximum and determine the populastion X and Y at that instant.