Write an equation for Verhulst Pearl logistic Growth where N= Population density at a time t r= Intrinsic rate of natural increase K = Carrying capacity

"The population of a metro city experiences fluctuations in its population desity over a period of time." If 'N' is the population density at the time 't' , write the population density at the time 't+1'.

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

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) =initial no. of nuclei. The above equation after integration can be represented as lambda=(2.303)/(t)log((N_(0))/(N)) Half-life period of U is 2.5xx10^(5) years. In how much time will the amount of U^(237) remaining be only 25% of the original amount ? a) 2.5xx10^(5) year b) 1.25xx10^(5) years c) 5xx10^(5) years d) none of these

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)) What is the activity in Ci (curie) of 1.0mole plutonium -239 ? (t_(1//2)=24000 years) a) 1.49 Ci b) 14.9 Ci c) 5.513xx10^(11) Ci d) None of these

Two consecutive irreversible first order reactions can be represented by Aoverset(k_(1))(rarr)Boverset(k_(2))(rarr)C The rate equation for A is readily interated to obtain [A]_(t)=[A]_(0).e^(-k_(1(t))) , and [B]_(t)=(k_(1)[A]_(0))/(k_(2)-k_(1))[e^(-k_(1)(t))-e^(-k_(2)(t))] Select the correct statement for given reaction: a) A decreases linearly b) B rise to a max. and then constant c) B rises to a max and the falls d) The slowest rate of increases of C occuring where B is max

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.

The integrated rate equations can be fitted with kinetic data to determine the order of a reaction. The integrated rate equations for zero, first and second order reactions are : Zero order : [Al =-kt+ [A]_0 First order : log [A] = -(kt)/2.303 + log [A]_0 Second order : 1/([A])=kt+1/[A]_0 These equations can also be used to calculate the halt life periods of different reactions, which give the time during which the concentration of a reactant is reduced to half of its initial concentration, i.e, at time t_(1//2), [A] = [A]_0//2 Answer the following (1 to 5) question : The decomposition of nitrogen pentoxide : 2N_2O_5(g) rarr 4NO_2(g) + O_2(g) is a first order reaction. The plot of log [N_2O_5] vs time (min) has slope = - 0.01389. The rate constant k is

When does the growth rate of a population following logistic model equal zero? The logistic model is given as dN/dt=rN(K-N/K).

In a p-n junction diode, the current I can be expressed as I = I_0 exp ((eV)/(2k_BT)) where I_0 is called the reverse saturation current, V is the voltage across the diode and is positive for forward bias and negative for reverse bias, and I is the current through the diode, k_B is the Boltzmann constant (8.6xx 10^-5 (eV)/K) and T is the absolute temperature. If for a given diode I_0 = 5 xx 10^-12 A and T = 300 K, then - What will be the increase in the current if the voltage across the diode is increased from 0.6 V to 0.7 V?

In a p-n junction diode, the current I can be expressed as I = I_0 exp ((eV)/(2k_BT)) where I_0 is called the reverse saturation current, V is the voltage across the diode and is positive for forward bias and negative for reverse bias, and I is the current through the diode, k_B is th Boltzmann constant (8.6xx 10^-5 (eV)/K) and T is the absolute temperature. If for a given diode I_0 = 5 xx 10^-12 A and T = 300 K, then - What is the dynamic resistance when the voltage is increased to 0.7 V from 0.6 V?