Mean lives of a radioactive sample are 30 years and 60 years for α -emission and β -emission respe

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13.Nuclei

medium

The mean lives of a radioactive sample are $30$ years and $60$ years for $\alpha$-emission and $\beta $ -emission respectively. If the sample decays both by $\alpha$- emission and $\beta $-emission simultaneously, the time after which, only one-fourth of the sample remain is :- ........... $years$

$10$

$20$

$40$

$45$

Solution

${\lambda _{(\alpha + \beta )}} = {\lambda _\alpha } + {\lambda _\beta }$

$ \Rightarrow \frac{1}{{{T_{\frac{1}{2}(\alpha – \beta )}}}} = \frac{1}{{{T_{\frac{1}{2}(\alpha )}}}} + \frac{1}{{{T_{\frac{1}{2}\left( \beta \right)}}}}$

$\Rightarrow \frac{1}{T_{\frac{1}{2}(x+\beta)}}=\frac{1}{30}+\frac{1}{60}=\frac{1}{20}$

$\therefore {{\rm{T}}_{\frac{1}{2}(\alpha + \beta )}} = 20$ years.

$\therefore $ One-fourth of sample will remain after $2$ half life $=40$ years.

Standard 12

Physics

In a $RA$ element the fraction of initiated amount remaining after its mean life time is

medium

State the relation between average life and decay constant.

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At time $t=0$, a material is composed of two radioactive atoms ${A}$ and ${B}$, where ${N}_{{A}}(0)=2 {N}_{{B}}(0)$ The decay constant of both kind of radioactive atoms is $\lambda$. However, A disintegrates to ${B}$ and ${B}$ disintegrates to ${C}$. Which of the following figures represents the evolution of ${N}_{{B}}({t}) / {N}_{{B}}(0)$ with respect to time $t$ ?

${N}_{{A}}(0)={No} . \text { of } {A} \text { atoms at } {t}=0$

${N}_{{B}}(0)={No} . \text { of } {B} \text { atoms at } {t}=0$

hard

(JEE MAIN-2021)

A sample contains $10^{-2}\, kg$ each of two substances A and $B$ with half lives $4 \,s$ and $8 \,s$ respectively. The ratio of then atomic weights is $1: 2$ The ratio of the amounts of $A$ and $B$ after $16 \,s$ is $\frac{x}{100}$. the value of $x$ is……..

medium

(JEE MAIN-2022)

$A$ and $B$ are two radioactive substances whose half lives are $1$ and $2$ years respectively. Initially $10\, gm$ of $A$ and $1\, gm$ of $B$ is taken. The time (approximate) after which they will have same quantity remaining is ……….. $years$

hard

The mean lives of a radioactive sample are $30$ years and $60$ years for $\alpha$-emission and $\beta $ -emission respectively. If the sample decays both by $\alpha$- emission and $\beta $-emission simultaneously, the time after which, only one-fourth of the sample remain is :- ........... $years$

Solution

Similar Questions

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