There are three lumps of a given radioactive | vedclass

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

Question

(A) The activity $A$ of a radioactive substance is given by $A = \lambda N$, where $\lambda$ is the decay constant and $N$ is the number of radioactiv

Vedclass · Accepted Answer

$1 : 2 : 3$

Vedclass · Answer

(A) The activity $A$ of a radioactive substance is given by $A = \lambda N$, where $\lambda$ is the decay constant and $N$ is the number of radioactive nuclei present at time $t$.The number of nuclei at time $t$ is given by $N(t) = N_0 e^{-\lambda t}$.Therefore, the activity at time $t$ is $A(t) = \lambda N_0 e^{-\lambda t} = A_0 e^{-\lambda t}$, where $A_0$ is the initial activity.Since all three lumps are of the same radioactive substance, they share the same decay constant $\lambda$.If the initial activities are $A_{01}, A_{02}, A_{03}$ in the ratio $1 : 2 : 3$, then at any later time $t$, the activities will be $A_1(t) = A_{01} e^{-\lambda t}$, $A_2(t) = A_{02} e^{-\lambda t}$, and $A_3(t) = A_{03} e^{-\lambda t}$.The ratio of their activities at time $t$ will be $A_1(t) : A_2(t) : A_3(t) = (A_{01} e^{-\lambda t}) : (A_{02} e^{-\lambda t}) : (A_{03} e^{-\lambda t}) = A_{01} : A_{02} : A_{03} = 1 : 2 : 3$.Thus, the ratio remains constant over time.

There are three lumps of a given radioactive substance. Their activity is in the ratio of $1 : 2 : 3$ now. What will be the ratio of their activities at any further date?

Similar Questions

If the image of $\left(\frac{-7}{5}, \frac{-6}{5}\right)$ in a line is $(1, 2)$,then the equation of the line is

$A$ whistle of frequency $540 \ Hz$ rotates in a horizontal circle of radius $2 \ m$ at an angular speed of $15 \ rad/s$. What is the highest frequency heard by a listener at rest with respect to the centre of the circle (in $Hz$)? (Velocity of sound in air $= 330 \ m/s$)

If $\frac{x}{(x - 1)(x^2 + 1)^2} = \frac{1}{4}\left[ \frac{1}{(x - 1)} - \frac{x + 1}{x^2 + 1} \right] + y$,then $y =$

Which of the following is incorrect regarding $H_2O_2$?

Which type of chromosome is shown in the figure below?

Vedclass Test Series

Exam Paper Generator

Online Exam Module