A radioactive nucleus can decay in two differ | vedclass

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

Question

(B) The decay constant $\lambda$ for a process is given by $\lambda = \frac{\ln 2}{T_{1/2}}$.For two parallel decay processes, the effective decay con

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(B) The decay constant $\lambda$ for a process is given by $\lambda = \frac{\ln 2}{T_{1/2}}$.For two parallel decay processes, the effective decay constant is $\lambda_{	ext{eff}} = \lambda_1 + \lambda_2$.Given $T_1 = 0.7 \ hr$ and $T_2 = 0.3 \ hr$, and $\ln 2 = 0.7$.Then $\lambda_1 = \frac{0.7}{0.7} = 1 \ hr^{-1}$ and $\lambda_2 = \frac{0.7}{0.3} = \frac{7}{3} \ hr^{-1}$.Effective decay constant $\lambda_{	ext{eff}} = 1 + \frac{7}{3} = \frac{10}{3} \ hr^{-1}$.The effective average life $	au_{	ext{eff}}$ is the reciprocal of the effective decay constant:$	au_{	ext{eff}} = \frac{1}{\lambda_{	ext{eff}}} = \frac{1}{10/3} = 0.3 \ hr$.Converting to minutes: $	au_{	ext{eff}} = 0.3 	imes 60 \ min = 18 \ min$.

$A$ radioactive nucleus can decay in two different processes with half-lives of $0.7 \ hr$ and $0.3 \ hr$. The effective average life of the nucleus in minutes is approximately (value of $\ln 2 = 0.7$):

Similar Questions

Define the decay constant and state its $SI$ unit.

$A$ sample of a radioactive element contains $8 \times 10^{16}$ active nuclei. The half-life of the element is $15 \text{ days}$. The number of nuclei decayed after $60 \text{ days}$ is:

Which sample,$A$ or $B$ shown in the figure,has a shorter mean-life?

Starting with a sample of pure ${}^{66}Cu$,$\frac{7}{8}$ of it decays into $Zn$ in $15 \ minutes$. The corresponding half-life is .......... $minutes$.

The decay constant of a radioactive sample is $\lambda$. The probability of decay per unit time is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module