Two radioactive substances X and Y initially | vedclass

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

Question

(C) Let $N_0$ be the initial number of nuclei for both $X$ and $Y$.Given half-lives: $T_{1/2, X} = 1\, h$ and $T_{1/2, Y} = 2\, h$.After time $t = 2\,

Vedclass · Accepted Answer

$1 : 1$

Vedclass · Answer

(C) Let $N_0$ be the initial number of nuclei for both $X$ and $Y$.Given half-lives: $T_{1/2, X} = 1\, h$ and $T_{1/2, Y} = 2\, h$.After time $t = 2\, h$,the number of nuclei remaining is given by $N = N_0 (1/2)^{t/T_{1/2}}$.For $X$: $N_X = N_0 (1/2)^{2/1} = N_0 / 4$.For $Y$: $N_Y = N_0 (1/2)^{2/2} = N_0 / 2$.Activity $A = \lambda N$,where $\lambda = \ln(2) / T_{1/2}$.Ratio of activities: $\frac{A_X}{A_Y} = \frac{\lambda_X N_X}{\lambda_Y N_Y} = \frac{(\ln 2 / T_{1/2, X}) N_X}{(\ln 2 / T_{1/2, Y}) N_Y} = \frac{T_{1/2, Y}}{T_{1/2, X}} 	imes \frac{N_X}{N_Y}$.Substituting the values: $\frac{A_X}{A_Y} = \frac{2}{1} 	imes \frac{N_0/4}{N_0/2} = 2 	imes \frac{1}{2} = 1$.Thus,the ratio is $1 : 1$.

Two radioactive substances $X$ and $Y$ initially contain equal number of nuclei. $X$ has a half-life of $1\, hour$ and $Y$ has a half-life of $2\, hours$. After $2\, hours$,the ratio of the activity of $X$ to the activity of $Y$ is

Similar Questions

$A$ radioactive sample $S_1$ having an activity $5 \mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10 \mu Ci$. The half-lives of $S_1$ and $S_2$ can be

The radioactive sources $A$ and $B$ have half-lives of $2 \ hr$ and $4 \ hr$ respectively,and initially contain the same number of radioactive atoms. At the end of $8 \ hr$,what is the ratio of their rates of disintegration?

What is the mass of $1 \, \text{curie}$ of $U^{234}$?

The half-life of a radioactive substance is $3.6$ days. How much of $20\, mg$ of this radioactive substance will remain after $36$ days?

Vedclass Test Series

Exam Paper Generator

Online Exam Module