The radioactivity of a sample is R_1 at a tim | vedclass

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

Question

(D) The activity of a radioactive sample is given by $R = N \lambda$,where $N$ is the number of radioactive nuclei and $\lambda$ is the decay constant

Vedclass · Accepted Answer

$(R_1 - R_2)$

Vedclass · Answer

(D) The activity of a radioactive sample is given by $R = N \lambda$,where $N$ is the number of radioactive nuclei and $\lambda$ is the decay constant.The decay constant $\lambda$ is related to the half-life $T$ by $\lambda = \frac{\ln 2}{T}$.At time $T_1$,the activity is $R_1 = N_1 \lambda$,so $N_1 = \frac{R_1}{\lambda} = \frac{R_1 T}{\ln 2}$.At time $T_2$,the activity is $R_2 = N_2 \lambda$,so $N_2 = \frac{R_2}{\lambda} = \frac{R_2 T}{\ln 2}$.The number of atoms that have disintegrated in the time interval $(T_2 - T_1)$ is the difference in the number of nuclei present at these times: $\Delta N = N_1 - N_2$.Substituting the expressions for $N_1$ and $N_2$:$\Delta N = \frac{R_1 T}{\ln 2} - \frac{R_2 T}{\ln 2} = \frac{T}{\ln 2} (R_1 - R_2)$.Since $T$ and $\ln 2$ are constants,the number of disintegrated atoms is proportional to $(R_1 - R_2)$.

The radioactivity of a sample is $R_1$ at a time $T_1$ and $R_2$ at a time $T_2$. If the half-life of the specimen is $T$,the number of atoms that have disintegrated in the time $(T_2 - T_1)$ is proportional to

Similar Questions

Radioactive nuclei $P$ and $Q$ disintegrate into $R$ with half-lives $1$ month and $2$ months respectively. At time $t=0$,the number of nuclei of each $P$ and $Q$ is $x$. At the time when the rates of disintegration of $P$ and $Q$ are equal,the number of nuclei of $R$ is ........ $x$.

Two radioactive substances $A$ and $B$ have decay constants $5\lambda$ and $\lambda$ respectively. At $t = 0$,a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $(1/e)^2$ will be

Half-lives of two radioactive elements $A$ and $B$ are $20 \ min$ and $40 \ min$,respectively. Initially,the samples have equal number of nuclei. After $80 \ min$,the ratio of decayed number of $A$ and $B$ nuclei will be

The variation of decay rate with the number of active nuclei is correctly shown in which graph?

$A$ 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...........$\%$

Vedclass Test Series

Exam Paper Generator

Online Exam Module