A radioactive nucleus is being produced at a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The rate of change of the number of nuclei $N$ is given by the differential equation: $\frac{dN}{dt} = \alpha - \lambda N$.At the maximum number o

Vedclass · Accepted Answer

$\frac{\alpha}{\lambda}$

Vedclass · Answer

(A) The rate of change of the number of nuclei $N$ is given by the differential equation: $\frac{dN}{dt} = \alpha - \lambda N$.At the maximum number of nuclei,the rate of change is zero,i.e.,$\frac{dN}{dt} = 0$.Setting the equation to zero: $0 = \alpha - \lambda N$.Solving for $N$,we get $N_{max} = \frac{\alpha}{\lambda}$.Note that if the initial number of nuclei $N_0$ is already greater than $\frac{\alpha}{\lambda}$,the number of nuclei will decrease until it reaches the equilibrium value $\frac{\alpha}{\lambda}$. If $N_0 < \frac{\alpha}{\lambda}$,it will increase until it reaches $\frac{\alpha}{\lambda}$.

$A$ radioactive nucleus is being produced at a constant rate $\alpha$ per second. Its decay constant is $\lambda$. If $N_0$ is the number of nuclei at time $t = 0$,then the maximum number of nuclei possible is:

Similar Questions

$N$ atoms of a radioactive element emit $n$ alpha particles per second. The half-life of the element is:

The half-life of a radioactive nucleus is $50$ days. The time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it had decayed and the time $t_1$ when $\frac{1}{3}$ of it had decayed is (in days):

The mean life time of a radionuclide,if its activity decreases by $4\%$ for every $1 \ h$,would be .......... $h$ (product is non-radioactive,i.e.,stable).

The activity of a radioactive sample is $I_0$ counts/minute at $t = 0$ and $I_0/e$ counts/minute at $t = 5$ minutes. At what time (in minutes) will its activity decrease to half of its initial value?

The half-life of a radioactive element is $10 \ h$. The fraction of initial radioactivity of the element that will remain after $40 \ h$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module