Show that decay rate R of a sample of a radio-nuclide is related to the number of radioactive nuclei N at that instant by the expression `R=lambdaN`.

Draw a graph showing the variation of decay rate with number of active nuclei.

State the law of radioactive decay, If N_0 is the number of radioactive nuclei in the sample at same initial time, find out the relation to determine the number N present at a subsequent time. Draw a plot of N as a function of time.

Explain,how radioactive nuclei can emit beta- particles even though nuclei do not contain these particles.Hence explain why the mass number of a radioactive nuclide does not charge during beta decay.

Show that the relation ‘>’ on the set R of all real numbers is transitive but it is neither reflexive nor symmetric.

Radioactive disintegration is a first order reaction and its rate depends only upon the nature of nucleus and does not depend upon external factors like temperature and pressure. The rate of radioactive disintegration (Activity) is represented as -(dN)/(dt)=lambdaN Where lambda= decay constant, N= number of nuclei at time t, N_(0) =intial no. of nuclei. The above equation after integration can be represented as lambda=(2.303)/(t)log((N_(0))/(N)) Calculate the half-life period of a radioactive element which remains only 1//16 of its original amount in 4740 years: a) 1185 years b) 2370 years c) 52.5 years d) none of these

Show that the relation R defined by (a, b) R(c,d)implies a+d=b+c in the set N is an equivalence relation.