For a radioactive material, its activity $A$ and rate of change of its activity $R$ are defined as $A=-\frac{d N}{d t}$ and $R=-\frac{d A}{d t}$, where $N(t)$ is the number of nuclei at time $t$. Two radioactive sources $P$ (mean life $\tau$ ) and $Q$ (mean life $2 \tau$ ) have the same activity at $t=0$. Their rates of change of activities at $t=2 \tau$ are $R_p$ and $R_Q$, respectively. If $\frac{R_p}{R_Q}=\frac{n}{e}$, then the value of $n$ is
For a radioactive material, its activity $A$ and rate of change of its activity $R$ are defined as $A=-\frac{d N}{d t}$ and $R=-\frac{d A}{d t}$, where $N(t)$ is the number of nuclei at time $t$. Two radioactive sources $P$ (mean life $\tau$ ) and $Q$ (mean life $2 \tau$ ) have the same activity at $t=0$. Their rates of change of activities at $t=2 \tau$ are $R_p$ and $R_Q$, respectively. If $\frac{R_p}{R_Q}=\frac{n}{e}$, then the value of $n$ is
- [IIT 2015]
- A
$1$
- B
$2$
- C
$3$
- D
$4$
Similar Questions
A radio isotope $X$ with a half-life $1.4 \times 10^{9}\; years$ decays of $Y$ which is stable. A sample of the rock from a cave was found to contain $X$ and $Y$ in the ratio $1: 7$. The age of the rock is ........ $ \times 10^9\; years$
A radio isotope $X$ with a half-life $1.4 \times 10^{9}\; years$ decays of $Y$ which is stable. A sample of the rock from a cave was found to contain $X$ and $Y$ in the ratio $1: 7$. The age of the rock is ........ $ \times 10^9\; years$
- [AIPMT 2014]
$99\%$ of a radioactive element will decay between
$99\%$ of a radioactive element will decay between
The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an
The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an
- [AIPMT 2009]
The count rate of a Geiger- Muller counter for the radiation of a radioactive material of half life of $30\, minutes$ decreases to $5\,{s^{ - 1}}$ after $2\, hours.$ The initial count rate was..........${s^{ - 1}}$
The count rate of a Geiger- Muller counter for the radiation of a radioactive material of half life of $30\, minutes$ decreases to $5\,{s^{ - 1}}$ after $2\, hours.$ The initial count rate was..........${s^{ - 1}}$
- [AIPMT 1995]
The decay constant of a radioactive element is $1.5 \times {10^{ - 9}}$ per second. Its mean life in seconds will be
The decay constant of a radioactive element is $1.5 \times {10^{ - 9}}$ per second. Its mean life in seconds will be