90% of a radioactive sample is left undecayed | vedclass

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

Question

(B) Let the initial amount of the radioactive sample be $N_0$.After time $t$,the amount remaining undecayed is $N(t) = 0.9 N_0$.According to the law o

Vedclass · Accepted Answer

$19$

Vedclass · Answer

(B) Let the initial amount of the radioactive sample be $N_0$.After time $t$,the amount remaining undecayed is $N(t) = 0.9 N_0$.According to the law of radioactive decay,$N(t) = N_0 e^{-\lambda t}$.Thus,$e^{-\lambda t} = 0.9$.After a total time $2t$,the amount remaining undecayed is $N(2t) = N_0 e^{-\lambda (2t)} = N_0 (e^{-\lambda t})^2$.Substituting the value of $e^{-\lambda t}$,we get $N(2t) = N_0 (0.9)^2 = 0.81 N_0$.The amount that has decayed in time $2t$ is $N_0 - N(2t) = N_0 - 0.81 N_0 = 0.19 N_0$.Therefore,the percentage of the initial sample that decays in time $2t$ is $19\%$.

$90\%$ of a radioactive sample is left undecayed after time $t$ has elapsed. What percentage of the initial sample will decay in a total time $2t$ : ..............$\%$

Similar Questions

At a given instant,there are $25\%$ undecayed radioactive nuclei in a sample. After $10 \, s$,the number of undecayed nuclei reduces to $6.25\%$. The mean life of the nuclei is...........$ s$.

$99\%$ of the nuclei of a radioactive element decay between which of the following times?

At time $t=0$ some radioactive gas is injected into a sealed vessel. At time $T$ some more of the gas is injected into the vessel. Which one of the following graphs best represents the logarithm of the activity $A$ of the gas with time $t$?

$A$ radioactive sample decays by $\beta$-emission. In the first $2 \ s$,$n$ $\beta$-particles are emitted,and in the next $2 \ s$,$0.25n$ $\beta$-particles are emitted. The half-life of the radioactive nuclei is ...... $s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module