The half-life period of a radioactive element | vedclass

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

Question

(C) Given that the half-life of $X$ is equal to the mean life of $Y$: $({T_{1/2}})_X = ({	au})_Y$ We know that ${T_{1/2}} = \frac{0.693}{\lambda}$ an

Vedclass · Accepted Answer

$Y$ will decay at a faster rate than $X$.

Vedclass · Answer

(C) Given that the half-life of $X$ is equal to the mean life of $Y$: $({T_{1/2}})_X = ({	au})_Y$ We know that ${T_{1/2}} = \frac{0.693}{\lambda}$ and ${	au} = \frac{1}{\lambda}$. Substituting these,we get: $\frac{0.693}{\lambda_X} = \frac{1}{\lambda_Y}$ $\Rightarrow \lambda_X = 0.693 \lambda_Y$ Since $0.693 The rate of decay is given by $R = \lambda N$. Initially,the number of atoms $N$ is the same for both. Since $\lambda_Y > \lambda_X$,the decay rate $R_Y = \lambda_Y N$ will be greater than $R_X = \lambda_X N$. Therefore,$Y$ will decay at a faster rate than $X$.

The half-life period of a radioactive element $X$ is the same as the mean life time of another radioactive element $Y$. Initially,both of them have the same number of atoms. Then:

Similar Questions

Give the equation form of the exponential law of radioactive decay.

Half-life period of a sample is $15$ years. How long will it take to decay $96.875\%$ of the sample?

For a substance,the average life for $\alpha$-emission is $1620 \ years$ and for $\beta$-emission is $405 \ years$. After how much time will $\frac{1}{4}$ of the material remain due to simultaneous emission?

If the half-life of a radioactive nucleus is $3$ days, nearly what fraction of the initial number of nuclei will decay on the third day? (Given, $\sqrt[3]{0.25} \approx 0.63$)

An archaeologist analyses the wood in a prehistoric structure and finds that the ratio of $C^{14}$ (half-life $= 5700 \, years$) to $C^{12}$ is only one-fourth of that found in the cells of buried plants. The age of the wood is about .......... $years$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module