A radioactive sample consists of two distinct species having equal number of atoms initially. The mean life time of one species is $\tau$ and that of the other is $5 \tau$. The decay products in both cases are stable. A plot is made of the total number of radioactive nuclei as a function of time. Which of the following figures best represents the form of this plot

  • [IIT 2001]
  • A
    159-a4
  • B
    159-b4
  • C
    159-c4
  • D
    159-d4

Similar Questions

The nuclide $^{131}I$ is radioactive, with a half-life of $8.04$ days. At noon on January $1$, the activity of a certain sample is $60089$. The activity at noon on January $24$ will be

A sample of radioactive element has a mass of $10\, gm$ at an instant $t = 0$.The approximate mass of this element in the sample after two mean lives is ..........$gm$

  • [AIPMT 2003]

A parent nucleus $X$ is decaying into daughter nucleus $Y$ which in turn decays to $Z$. The half lives of $X$ and $Y$ are $40000 \,yr$ and $20 \,yr$, respectively. In a certain sample, it is found that the number of $Y$ nuclei hardly changes with time. If the number of $X$ nuclei in the sample is $4 \times 10^{20}$, the number of $Y$ nuclei present in it is

  • [KVPY 2012]

In a radioactive decay process, the activity is defined as $A=-\frac{\mathrm{d} N}{\mathrm{~d} t}$, where $N(t)$ is the number of radioactive nuclei at time $t$. Two radioactive sources, $S_1$ and $S_2$ have same activity at time $t=0$. At a later time, the activities of $S_1$ and $S_2$ are $A_1$ and $A_2$, respectively. When $S_1$ and $S_2$ have just completed their $3^{\text {rd }}$ and $7^{\text {th }}$ half-lives, respectively, the ratio $A_1 / A_2$ is. . . . . . .

  • [IIT 2023]

The decay constant for a radioactive nuclide is $1.5 \times 10^{-5} s ^{-1}$. Atomic of the substance is $60\,g$ mole $^{-1},\left( N _{ A }=6 \times 10^{23}\right)$. The activity of $1.0\,\mu g$ of the substance is $.......\,\times 10^{10}\,Bq$

  • [JEE MAIN 2023]