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

$A$ radioactive element which can decay by two processes has half-life $t_1$ for the first process and half-life $t_2$ for the second process. Let $\langle t \rangle$ be the effective average-life of this element. Which of the following is correct?

$A$ radioactive sample $S_{1}$ having the activity $A_{1}$ has twice the number of nuclei as another sample $S_{2}$ of activity $A_{2}$. If $A_{2} = 2 A_{1}$,then the ratio of half-life of $S_{1}$ to the half-life of $S_{2}$ is

$A$ radioactive source has a half-life of $6 \,h$. $A$ freshly prepared sample of the same exhibits radioactivity $32$ times the permissible safe value. The minimum time after which it would be possible to work safely with the source is (in $\,h$)

Two radioactive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0$,they have the same number of nuclei. The ratio of the number of nuclei of $A$ to those of $B$ will be $(1/e)^2$ after a time interval of:

The half-life of tritium is $ 12.5 $ years. What mass of tritium of initial mass $ 64 \ mg $ will remain undecayed after $ 50 $ years (in $mg$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module