Two radioactive substances X and Y originally have N _{1} and N

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13.Nuclei

hard

Two radioactive substances $X$ and $Y$ originally have $N _{1}$ and $N _{2}$ nuclei respectively. Half life of $X$ is half of the half life of $Y$. After three half lives of $Y$, number of nuclei of both are equal. The ratio $\frac{ N _{1}}{ N _{2}}$ will be equal to

$\frac{1}{8}$

$\frac{3}{1}$

$\frac{8}{1}$

$\frac{1}{3}$

(JEE MAIN-2021)

Solution

$T _{ x }= t ; T _{ y }=2 t$

$3 T _{ y }=6 t$

$N _{1}^{\prime}= N _{2}^{\prime}$

$N _{1} e ^{-\lambda_{1} 6 t }= N _{2} e ^{-\lambda_{2} 6 t }$

$\frac{ N _{1}}{ N _{2}}= e ^{\left(\lambda_{1}-\lambda_{2}\right) 6 t }= e ^{\ln 2\left(\frac{1}{t}-\frac{1}{2 t }\right) \times 6 t }= e ^{(1 n 2) \times 3}= e ^{ ln 8}=8$

$\frac{ N _{1}}{ N _{2}}=\frac{8}{1}$

Standard 12

Physics

Two radioactive materials $A$ and $B$ have decay constants $10\,\lambda $ and $\lambda $, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of a to that of $B$ will be $1/e$ after a time

medium

(JEE MAIN-2019)

The energy spectrum of $\beta$-particles [number $N(E)$ as a function of $\beta$-energy $E$] emitted from a radioactive source is

easy

(AIEEE-2006)

Half life of a radioactive element is $10\, days$. The time during which quantity remains $1/10$ of initial mass will be ………$days$

easy

Half-life of a radioactive substance is $20$ minutes. Difference between points of time when it is $33\%$ disintegrated and $67\%$ disintegrated is approximately ……….. $min$

hard

(AIIMS-2000)

Deuteron is a bound state of a neutron and a proton with a binding energy $B = 2.2\, MeV$. A $\gamma $ -ray of energy $E$ is aimed at a deuteron nucleus to try to break it into a (neutron + proton) such that the $n$ and $p$ move in the direction of the incident $\gamma $ -ray. If $E = B$, show that this cannot happen. Hence calculate how much bigger than $B$ must $E$ be for such a process to happen.

hard

Two radioactive substances $X$ and $Y$ originally have $N _{1}$ and $N _{2}$ nuclei respectively. Half life of $X$ is half of the half life of $Y$. After three half lives of $Y$, number of nuclei of both are equal. The ratio $\frac{ N _{1}}{ N _{2}}$ will be equal to

Solution

Similar Questions

Two radioactive materials $A$ and $B$ have decay constants $10\,\lambda $ and $\lambda $, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of a to that of $B$ will be $1/e$ after a time

The energy spectrum of $\beta$-particles [number $N(E)$ as a function of $\beta$-energy $E$] emitted from a radioactive source is

Half life of a radioactive element is $10\, days$. The time during which quantity remains $1/10$ of initial mass will be ………$days$

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