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

(B) The half-life of $X$ is $T_{1/2, X} = \frac{0.693}{\lambda_X}$.The mean life of $Y$ is $	au_Y = \frac{1}{\lambda_Y}$.Given $T_{1/2, X} = 	au_Y$,

Vedclass · Accepted Answer

$Y$ will decay faster than $X$

Vedclass · Answer

(B) The half-life of $X$ is $T_{1/2, X} = \frac{0.693}{\lambda_X}$.The mean life of $Y$ is $	au_Y = \frac{1}{\lambda_Y}$.Given $T_{1/2, X} = 	au_Y$,we have $\frac{0.693}{\lambda_X} = \frac{1}{\lambda_Y}$,which implies $\frac{\lambda_X}{\lambda_Y} = 0.693$.The decay rate $R$ is given by $R = \lambda N$.Given initial number of atoms $N_X = N_Y = N_0$,the initial decay rates are $R_X = \lambda_X N_0$ and $R_Y = \lambda_Y N_0$.Taking the ratio,$\frac{R_X}{R_Y} = \frac{\lambda_X}{\lambda_Y} = 0.693$.Since $0.693 < 1$,it follows that $R_X < R_Y$,meaning $Y$ decays faster than $X$ initially.

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

Similar Questions

An ancient discovery found a sample where $75 \%$ of the original carbon $(C^{14})$ remains. The age of the sample is: $\left(T_{1/2}(C^{14}) = 5730 \text{ years}, \ln 0.5 = -0.7, \ln 0.75 = -0.3\right)$ (in $\text{ years}$)

Half-lives of two radioactive nuclei $A$ and $B$ are $10 \, minutes$ and $20 \, minutes$,respectively. If,initially,a sample has an equal number of nuclei,then after $60 \, minutes$,the ratio of the number of decayed nuclei of $A$ and $B$ will be:

In a radioactive material,the activity at time $t_{1}$ is $R_{1}$ and at a later time $t_{2}$,it is $R_{2}$. If the decay constant of the material is $\lambda$,then:

The half-life of radon is $3.8 \ days$. Three-fourths of a radon sample decays in ............ $days$.

$10 \, g$ of radioactive material of half-life $15 \, \text{years}$ is kept in store for $20 \, \text{years}$. The disintegrated material is ............ $g$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module