A mixture consists of two radioactive materia | vedclass

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

Question

(D) Let the amount of $A_1$ and $A_2$ become equal after $t \, s$.The amount of a radioactive substance remaining after time $t$ is given by $N = N_0

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(D) Let the amount of $A_1$ and $A_2$ become equal after $t \, s$.The amount of a radioactive substance remaining after time $t$ is given by $N = N_0 \left( \frac{1}{2} \right)^{t/T_{1/2}}$,where $T_{1/2}$ is the half-life.For $A_1$: $N_1 = 40 \left( \frac{1}{2} \right)^{t/20}$.For $A_2$: $N_2 = 160 \left( \frac{1}{2} \right)^{t/10}$.Setting $N_1 = N_2$:$40 \left( \frac{1}{2} \right)^{t/20} = 160 \left( \frac{1}{2} \right)^{t/10}$.Dividing both sides by $40$:$\left( \frac{1}{2} \right)^{t/20} = 4 \left( \frac{1}{2} \right)^{t/10}$.Using the property $2^{-x} = \frac{1}{2^x}$:$\frac{1}{2^{t/20}} = 4 \cdot \frac{1}{2^{t/10}}$.Rearranging the terms:$\frac{2^{t/10}}{2^{t/20}} = 4$.$2^{(t/10 - t/20)} = 2^2$.Equating the exponents:$\frac{t}{10} - \frac{t}{20} = 2$.$\frac{2t - t}{20} = 2$.$\frac{t}{20} = 2 \Rightarrow t = 40 \, s$.

$A$ mixture consists of two radioactive materials $A_1$ and $A_2$ with half-lives of $20 \, s$ and $10 \, s$ respectively. Initially,the mixture has $40 \, g$ of $A_1$ and $160 \, g$ of $A_2$. The amount of the two in the mixture will become equal after how many seconds (in $, s$)?

Similar Questions

The sample of a radioactive substance has $10^6$ nuclei. Its half-life is $20 \, s$. The number of nuclei that will be left after $10 \, s$ is nearly ...... $\times 10^5$.

The relation between $\lambda$ and $T_{1/2}$ is ($T_{1/2} = \text{half-life}$,$\lambda = \text{decay constant}$)

Activity of a radioactive sample is $R_1$ at a time $t_1$ and $R_2$ at a time $t_2$. Its half-life period is $T$. The number of atoms that have disintegrated in the time interval $(t_2 - t_1)$ is equal to $\frac{n(R_1 - R_2)T}{\ln 4}$. Then '$n$' is equal to

$x$ fraction of a radioactive sample decays in $t$ time. What fraction will decay in $2t$ time?

The half-life of a radioactive substance is $5$ years. What is the probability of decay of this element in $10$ years?

Vedclass Test Series

Exam Paper Generator

Online Exam Module