Two radioactive substances X and Y originally | vedclass

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

Question

(C) Let the half-life of $X$ be $T_{x} = t$ and the half-life of $Y$ be $T_{y} = 2t$.After three half-lives of $Y$,the time elapsed is $t_{total} = 3

Vedclass · Accepted Answer

$\frac{8}{1}$

Vedclass · Answer

(C) Let the half-life of $X$ be $T_{x} = t$ and the half-life of $Y$ be $T_{y} = 2t$.After three half-lives of $Y$,the time elapsed is $t_{total} = 3 	imes T_{y} = 3 	imes 2t = 6t$.Using the radioactive decay law $N(t) = N_{0} \left(\frac{1}{2}ight)^{t/T}$,the number of nuclei remaining for $X$ and $Y$ are:$N_{1}' = N_{1} \left(\frac{1}{2}ight)^{6t/t} = N_{1} \left(\frac{1}{2}ight)^{6} = \frac{N_{1}}{64}$$N_{2}' = N_{2} \left(\frac{1}{2}ight)^{6t/2t} = N_{2} \left(\frac{1}{2}ight)^{3} = \frac{N_{2}}{8}$Given that $N_{1}' = N_{2}'$,we have:$\frac{N_{1}}{64} = \frac{N_{2}}{8}$$\frac{N_{1}}{N_{2}} = \frac{64}{8} = \frac{8}{1}$

Two radioactive substances $X$ and $Y$ originally have $N_{1}$ and $N_{2}$ nuclei respectively. The half-life of $X$ is half of the half-life of $Y$. After three half-lives of $Y$,the number of nuclei of both are equal. The ratio $\frac{N_{1}}{N_{2}}$ will be equal to:

Similar Questions

The half-life of a radioactive sample is $5 \,s$. If the initial mass of the sample is $60 \,g$, then the time required to reduce the sample to $7.5 \,g$ is (in $\,s$)

If $20 \, g$ of a radioactive substance reduces to $10 \, g$ due to radioactive decay in $4 \, minutes$, then in what time will $80 \, g$ of the same substance reduce to $10 \, g$?

The half-life of a radioactive element is $12.5 \; h$ and its initial quantity is $256 \; g$. After how much time (in $h$) will its quantity remain $1 \; g$?

$A$ radioactive material decays by simultaneous emission of two particles with respective half-lives $1620$ years and $810$ years. The time (in years) after which one-fourth of the material remains is:

If ${N_0}$ is the original mass of the substance of half-life period ${T_{1/2}} = 5 \text{ years}$,then the amount of substance left after $15 \text{ years}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module