A radioactive nucleus can decay by two differ | vedclass

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

Question

(B) The decay constant for the first process is $\lambda_1 = \frac{\ln 2}{T_1}$ and for the second process is $\lambda_2 = \frac{\ln 2}{T_2}$.Since th

Vedclass · Accepted Answer

$4762 	ext{ yr}$

Vedclass · Answer

(B) The decay constant for the first process is $\lambda_1 = \frac{\ln 2}{T_1}$ and for the second process is $\lambda_2 = \frac{\ln 2}{T_2}$.Since the nucleus decays by two processes, the effective decay constant is $\lambda = \lambda_1 + \lambda_2$.Substituting the expressions for decay constants, we get $\frac{\ln 2}{T} = \frac{\ln 2}{T_1} + \frac{\ln 2}{T_2}$, which simplifies to $\frac{1}{T} = \frac{1}{T_1} + \frac{1}{T_2}$.Thus, the effective half-life $T$ is given by $T = \frac{T_1 T_2}{T_1 + T_2}$.Given $T_1 = 5 	imes 10^3 	ext{ yr}$ and $T_2 = 10^5 	ext{ yr} = 100 	imes 10^3 	ext{ yr}$.$T = \frac{(5 	imes 10^3) 	imes (100 	imes 10^3)}{5 	imes 10^3 + 100 	imes 10^3} = \frac{500 	imes 10^6}{105 	imes 10^3} = \frac{500000}{105} \approx 4761.9 	ext{ yr}$.Rounding to the nearest integer, we get $4762 	ext{ yr}$.

$A$ radioactive nucleus can decay by two different processes. The half-lives of the first and second decay processes are $5 \times 10^3$ years and $10^5$ years respectively. Then, the effective half-life of the nucleus is

Similar Questions

Radon-$222$ has a half-life of $3.8$ days. If one starts with $0.064 \ kg$ of radon-$222$, the quantity of radon-$222$ left after $19$ days will be (in $kg$)

Two radioactive materials $A$ and $B$ have decay constants $25 \lambda$ and $16 \lambda$ respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $B$ to that of $A$ will be $e$ after a time $t = \frac{1}{a \lambda}$. The value of $a$ is $......$

$A$ radio isotope has a half-life of $75\, \text{years}$. The fraction of the atoms of this material that would decay in $150\, \text{years}$ will be...........$\%$

Two radioactive elements $A$ and $B$ initially have the same number of atoms. The half-life of $A$ is equal to the mean life of $B$. If $\lambda_A$ and $\lambda_B$ are the decay constants of $A$ and $B$ respectively,then choose the correct relation from the given options.

The decay constant of a radioactive substance is $0.173 \, (years)^{-1}.$ Therefore:

Vedclass Test Series

Exam Paper Generator

Online Exam Module