Let `lambda_(p)` and `lambda_(d)` be the decay constants of the parent and the daughter nuclei.If `N_(P)` and `N_(d)` be the number of parent and daughter nuclei at time `t` the condition that the daughter nuclei become constant is : `1) lambda_(p)N_(p)=lambda_(d)N_(d)` ` 2) lambda_(p)N_(d)=lambda_(d)N_(p) ` ` 3) lambda_(p)lambda_(d)=N_(p)N_(d)` 4) None of these

Suppose, the daughter nucleus in a nuclear decay is itself radioactive. Let lambda_p and lambda_d be the decay constants of the parent and the daughter nuclei. Also, let N_p and N_d be the number of parent and daughter nuclei at time t . Find the condition for which the number of daughter nuclei becomes constant.

A particular type of nucleus whose decay constant is lambda is produced at a steady rate of p nuclei per second. Show that the number of nuclei N present t second after the production starts is N=(P)/(lambda)[1-e^(~lambdat)] .

Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths lambda_(N) ,lambda_(A) respectively. The ratio (lambda_(N))/(lambda_(A)) is closest to :

A radioactive nuclide is produced at a constant rate of alpha per second . It’s decay constant is lambda . If N_(0) be the no. of nuclei at time t=0 , then max. no. nuclei possible are :

Uranium ._(92)^(238)U is an ustable nucleus. It decays to Thorium ._(92)^(238)Th , which is again an unstable nucleus which further decays to ._(91)^(234)Pa . Let ._(92)^(238)U be called A of decay constant lambda_(1) and ._(90)^(234)Th is called as B of decay constant lambda_(2) and stable nuclei ._(91)^(234)Pa be called as C . Here A is called parent nucleus and B is called daughter nucleus of A . Any two adjacent nuclei may be consider parent or daughter nuclei A, B and C respectively at time 't' . Then we can write Aoverset(lambda_(1))rarrBoverset(lambda_(2))rarrC Rate of disintergration of A=(dN_(1))/(dt)=lambda_(1)N_(1) Rate of disintergration of B=(dN_(2))/(dt)=lambda_(1)N_(1)-lambda_(2)N_(2) Rate of formation of nuclei C is equal to (dN_(3))/(dt)=lambda_(2)N_(2) If at t=0 , there are N_(0) number of nuclei of A where as nuclei B and C are absent in the sample Answer the following questions ltbgt Numeber of the nuclei of nuclei C at time t is

Uranium ._(92)^(238)U is an ustable nucleus. It decays to Thorium ._(92)^(238)Th , which is again an unstable nucleus which further decays to ._(91)^(234)Pa . Let ._(92)^(238)U be called A of decay constant lambda_(1) and ._(90)^(234)Th is called as B of decay constant lambda_(2) and stable nuclei ._(91)^(234)Pa be called as C . Here A is called parent nucleus and B is called daughter nucleus of A . Any two adjacent nuclei may be consider parent or daughter nuclei A, B and C respectively at time 't' . Then we can write Aoverset(lambda_(1))rarrBoverset(lambda_(2))rarrC Rate of disintergration of A=(dN_(1))/(dt)=lambda_(1)N_(1) Rate of disintergration of B=(dN_(2))/(dt)=lambda_(1)N_(1)-lambda_(2)N_(2) Rate of formation of nuclei C is equal to (dN_(3))/(dt)=lambda_(2)N_(2) If at t=0 , there are N_(0) number of nuclei of A where as nuclei B and C are absent in the sample Answer the following questions Number of nuclei of B at any time t is

Show that if lambda_(1), lambda_(2), ...., lamnda_(n) are n eigenvalues of a square matrix a of order n, then the eigenvalues of the matric A^(2) are lambda_(1)^(2), lambda_(2)^(2),..., lambda_(n)^(2) .