A sample of radioactive element containing $4 \times 10^{16}$ active nuclei. Half life of element is $10$ days, then number of decayed nuclei after $30$ days is ........ $\times 10^{16}$
A sample of radioactive element containing $4 \times 10^{16}$ active nuclei. Half life of element is $10$ days, then number of decayed nuclei after $30$ days is ........ $\times 10^{16}$
- [AIPMT 2002]
- A
$0.5$
- B
$2$
- C
$3.5$
- D
$1$
Similar Questions
Following statements related to radioactivity are given below
$(A)$ Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
$(B)$ The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
$(C)$ Slope of the graph of $\log _{e}$ (no. of undecayed nuclei) $Vs$. time represents the reciprocal of mean life time $(\tau)$.
$(D)$ Product of decay constant ( $\lambda$ ) and half-life time $\left(T_{1 / 2}\right)$ is not constant.
Choose the most appropriate answer from the options given below
Following statements related to radioactivity are given below
$(A)$ Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
$(B)$ The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
$(C)$ Slope of the graph of $\log _{e}$ (no. of undecayed nuclei) $Vs$. time represents the reciprocal of mean life time $(\tau)$.
$(D)$ Product of decay constant ( $\lambda$ ) and half-life time $\left(T_{1 / 2}\right)$ is not constant.
Choose the most appropriate answer from the options given below
- [JEE MAIN 2022]
A sample initially contains only $U -238$ isotope of uranium. With time, some of the $U -238$ radioactively decays into $Pb -206$ while the rest of it remains undisintegrated.
When the age of the sample is $P \times 10^8$ years, the ratio of mass of $Pb -206$ to that of $U -238$ in the sample is found to be $7$ . The value of $P$ is. . . . . .
[Given : Half-life of $U-238$ is $4.5 \times 10^9$ years; $\log _e 2=0.693$ ]
A sample initially contains only $U -238$ isotope of uranium. With time, some of the $U -238$ radioactively decays into $Pb -206$ while the rest of it remains undisintegrated.
When the age of the sample is $P \times 10^8$ years, the ratio of mass of $Pb -206$ to that of $U -238$ in the sample is found to be $7$ . The value of $P$ is. . . . . .
[Given : Half-life of $U-238$ is $4.5 \times 10^9$ years; $\log _e 2=0.693$ ]
- [IIT 2024]
Certain radioactive substance reduces to $25\%$ of its value in $16\ days$. Its half-life is .......... $days$
Certain radioactive substance reduces to $25\%$ of its value in $16\ days$. Its half-life is .......... $days$
A radioactive sample has ${N_0}$ active atoms at $t = 0$. If the rate of disintegration at any time is $R$ and the number of atoms is $N$, then the ratio $ R/N$ varies with time as
A radioactive sample has ${N_0}$ active atoms at $t = 0$. If the rate of disintegration at any time is $R$ and the number of atoms is $N$, then the ratio $ R/N$ varies with time as
There are two radionuclei $A$ and $B.$ $A$ is an alpha emitter and $B$ is a beta emitter. Their distintegration constants are in the ratio of $1 : 2.$ What should be the ratio of number of atoms of two at time $t = 0$ so that probabilities of getting $\alpha$ and $\beta$ particles are same at time $t = 0.$
There are two radionuclei $A$ and $B.$ $A$ is an alpha emitter and $B$ is a beta emitter. Their distintegration constants are in the ratio of $1 : 2.$ What should be the ratio of number of atoms of two at time $t = 0$ so that probabilities of getting $\alpha$ and $\beta$ particles are same at time $t = 0.$