[N_(t)=N_(0)" ert in which 'r' refers to

At time t = 0, a material is composed of two radioactive atoms A and B, where N_(A0) = 2N_(B0) . The decay constant of both kind of radioactive atoms is lamda . However, A disintegrates to B and B disintegrates to C. Which of the following figures represents the evolution of N_B(t)//N_B(0) with respect to time t? [ N_A(0)= No. of A atoms at t = 0] [ N_B(0)= No. of B atoms at t= 0 ]

Consider radioactive decay of A to B with which further decays either to X or Y , lambda_(1), lambda_(2) and lambda_(3) are decay constant for A to B decay, B to X decay and Bto Y decay respectively. At t=0 , the number of nuclei of A,B,X and Y are N_(0), N_(0) zero and zero respectively. N_(1),N_(2),N_(3) and N_(4) are the number of nuclei of A,B,X and Y at any instant t . At t=oo , which of following is incorrect ?

A thick spherical shell of inner and outer radii r and R respectively has thermal conductivity k = (rho)/(x^(n)) , where rho is a constant and x is distance from the centre of the shell. The inner and outer walls are maintained at temperature T_(1) and T_(2) (lt T_(1)) (a) Find the value of number n (call it n_(0) ) for which the temperature gradient remains constant throughout the thickness of the shell. (b) For n=n_(0) , find the value of x at which the temperature is (T_(1)+T_(2))/(2) (c) For n = n_(0) , calculate the rate of flow of heat through the shell.

If S_(n)=sum_(r =0)^(n)(r^(2)+r+1).r! then which is/are correct

The number of atoms of a radioactive substance of half-life T is N_(0) at t = 0. The time necessary to decay from N_(0)//2 atoms to N_(0)//10 atoms will be

If sum_(r=1)^(n)T_(r)=(n(n+1)(n+2)(n+3))/(12) where T_(r) denotes the rth term of the series. Find lim_(nto oo) sum_(r=1)^(n)(1)/(T_(r)) .

If t_(n)=an^(-1) , then find the value of n, given that a=2,r=3 and t_(n)=486 .

Let R_(t) represents activity of a sample at an insant and N_(t) represent number of active nuclei in the sample at the instant. T_(1//2) represents the half life. {:(,"Column I",,"Column II"),((A),t=T_(1//2),(p),R_(t)=(R_(0))/(2)),((B),t=(T_(1//2))/(ln2),(q),N_(0)-N_(t)=(N_(0))/(2)),((C),t=(3)/(2)T_(1//2),(r),(R_(t)-R_(0))/(R_(0)) = (1-e)/(e)),(,,(s),N_(t)=(N_(0))/(2sqrt(2))):}